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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. geometric Goppa codes; generalized algebraic geometry codes; code automorphisms; automorphism groups of function fields; algebraic function fields
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Chebotarev's theorem; Galois covering; smooth projective curves; function field; number of unramified points; Frobenius conjugacy class Kumar Murty, Vijaya; Scherk, John, Effective versions of the Chebotarev density theorem for function fields, C. R. Acad. Sci. Paris Sér. I Math., 319, 6, 523-528, (1994)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. fields of moduli; action of automorphism of reflex field on the torsion points; Abelian varieties with many complex multiplications; Abelian variety; cyclotomic fields; primes of good reduction; prime ideal decomposition of the endomorphism; Frobenius map; Riemann forms; field of definition; rank of a CM type; Langlands' conjecture; size of the Galois group of torsion points S. Lang, Complex multiplication. Berlin-Heidelberg-NewYork (1983). Zbl0536.14029 MR713612
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. monads; higher Chow complex; operads; unital \(k\)-algebras; little \(n\)-cubes operad; tensor category; braid algebras; mixed Tate motives; symmetric monoidal category; operad of spaces; iterated loop spaces; higher Chow groups; Adams operations; derived category; integral mixed Tate modules; derived categories of modules; DGA; triangulated category; Tannakian category; Hopf algebra; co-Lie algebra; Beilinson-Soulé conjecture; operadic tensor product; cellular approximation theorem Kriz, I.; May, J. P., Operads, algebras, modules and motives, Astérisque, 233, (1995), iv+145 pp
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Singularities; Complex analytic geometry; Proceedings; Symposium; Kyoto; RIMS; singularities in complex analytic geometry; complex affine root system; quartic surfaces of elliptic ruled type; bimeromorphic geometry of Gorenstein singularities; Torus embedding; cusp singularities; geometric genus; complex analytic foliation; Deligne, Gabber, Beilinson-Bernstein type theorem; singularities of nilpotent manifold; bifurcation set; Milnor number; quasi homogeneous polynomial; mapping singularities; Morse inequality
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. algebraic function field; tower of function fields; tensor rank; algorithm; finite field Pieltant, Julia; Randriam, Hugues, New uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields, Math. Comp., 0025-5718, 84, 294, 2023-2045, (2015)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. anisotropic quadratic forms; function fields of quadrics; Chow groups Karpenko, N., \textit{on the first Witt index of quadratic forms}, Invent. Math., 153, 455-462, (2003)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. algorithms in algebra; Gröbner bases; primary decomposition; syzygies; integral closure; degree of complexity; computation of cohomology; ideal transform; ring of invariants; Nullstellensätze; Macaulay; Hilbert function; radical; Jacobian ideal; computational aspects; JFM 52.0127.01 Vasconcelos, W.V.: Computational methods in commutative algebra and algebraic geometry. With chapters by David Eisenbud. Daniel R, Grayson, Jürgen Herzog and Michael Stillman, volume 2 of Algorithms and Computation in Mathematics. Springer, Berlin (1998)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. K3 surface over a finite field; Tate's conjecture on algebraic cycles; order of pole of zeta function; crystalline deformation theory; quasi-canonical varieties over p-adic fields; equicharacteristic deformations of abstract F-crystals Nygaard, Niels; Ogus, Arthur, Tate's conjecture for \(K3\) surfaces of finite height, Ann. of Math. (2), 0003-486X, 122, 3, 461-507, (1985)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. completely real algebraic variety; number of points in hypersurface; intersection; Bezout theorem
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. varieties; finite fields; small solutions of congruences; systems of forms; points in boxes; system of congruences
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. group of rational points; maximal anticyclotomic extension; elliptic curve; complex multiplication; L-function; Thue-Siegel-Roth theorem Rohrlich, D. E., \textit{on \textit{L}-functions of elliptic curves and anticyclotomic towers}, Invent. Math., 75, 383-408, (1984)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. hyperplane arrangements; Torelli theorem; unstable hyperplanes; Dolgachev sheaf of logarithmic differentials; logarithmic vector fields; stable curves Faenzi, Daniele; Matei, Daniel; Vallès, Jean, Hyperplane arrangements of Torelli type, Compos. Math., 149, 2, 309-332, (2013)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Euler characteristic; irreducible component of reduced algebraic curve; virtual singularity theorem; Miyaoka-Yau inequality Kojima, H.: On veys' conjecture. Indag. math. 10, 537-538 (1999)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. plane curve singularity; Artin-Greenberg function; value semigroup; tree of contacts; multiplicity; Puiseux expansions; characteristic exponents
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. number fields; anabelian geometry; Neukirch-Uchida theorem; densities of primes; stable sets of primes
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. p-adic height pairings; heights of abelian varieties; p-adic L-series; Birch--Swinnerton-Dyer formula for the Iwasawa L-function Schneider, P., \textit{ \textit{p}-adic height pairings. II}, Invent. Math., 79, 329-374, (1985)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. rational points over complex function fields; rationally connected manifolds; special manifolds; manifolds of general type
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Brauer groups; curves over local fields; \(p\)-adic curves; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields Saltman, D. J., Division algebras over \(p\)-adic curves, J. Ramanujan Math. Soc., 12, 25-47, (1997)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. absolute Galois groups; function fields of one variable; anabelian geometry F. Pop, ''On Grothendieck's conjecture of birational anabelian geometry,'' Ann. of Math., vol. 139, iss. 1, pp. 145-182, 1994.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. regular ring; global dimension; regularity for non-commutative rings; ring of differential operators; normal toric algebra; conic module; complete conic module; projective resolution; non-commutative resolution; non-commutative crepant resolution; simplicial algebra; chambers of constancy; hyperplane arrangement; acyclicity Lemma; Frobenius map; Kunz's Theorem; F-regularity; minimal model program; rational singularities
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. equidistribution; Riemann hypothesis for function fields R.W.K. Odoni , P.G. Spain , Equidistribution of values of rational functions (mod p) . Proc. R. Soc. Edinb . Sect. A 125 ( 1995 ), 911 - 929 . MR 1361624 | Zbl 0838.11077
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. tower of function fields; finite field; Artin-Schreier extension A. Garciaand H. Stichtenoth. Some Artin-Schreier towers are easy. Mosc.Math. J., 5 (2005), 767--774.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. topological spaces with involution; level; colevel; sublevel; affine varieties; Hopf problem; equivariant maps; Stiefel manifolds; Borsuk-Ulam theorem; topology of spheres; arithmetic of sums of squares in rings; quadratic forms; Pythagoras number; invariants; Radon-Hurwitz number; isotropic form; ring of continuous functions; anisotropic form Dai Z.D., Lam T.Y.: Levels in algebra and topology. Comment. Math. Helv. 59, 376--424 (1984)
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Tower of function fields; Genus; Rational places A. Garcia and H. Stichtenoth, Explicit towers of function fields over finite fields, In Topics in geometry, coding theory and cryptography , volume 6 of Algebr. Appl. , pages 1-58, Springer, Dordrecht, 2007.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. genus; towers of function fields; asymptotically bad towers
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Towers of function fields; congruence function fields; genus; rational places; limits of towers; Zink's bound; cubic finite fields; Artin--Schreier extensions; Drinfeld--Vlăduţ bound; Hasse--Weil bound. Bezerra, J.; Garcia, A.; Stichtenoth, H.: An explicit tower of function fields over cubic finite fields and Zink's lower bound for \(A(q3)\). J. reine angew. Math. 589, 159-199 (2005)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. multiplicity estimates; product theorem; diophantine approximation; zero theorems; intersection theory [14] Michael Nakamaye, &Multiplicity estimates and the product theorem&#xBull. Soc. Math. France123 (1995) no. 2, p.~155Numdam | &MR~13 | &Zbl~0841.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. ample divisor; tangential ramified marked covering; marked elliptic curve; elliptic solitons; theta divisor; Torelli-like theorem for compactified jacobians of tangential covers Armando Treibich, Compactified Jacobians of tangential covers, Integrable systems (Luminy, 1991) Progr. Math., vol. 115, Birkhäuser Boston, Boston, MA, 1993, pp. 39 -- 59.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Singlarity theory; semialgebraic sets; Artin's approximation theorem; finite determinacy; weighted homogeneous singularities; plane curve singularities; resolution of surface singularities A. Dimca, \textit{Topics on real and complex singularities: an introduction}, Advanced Lectures in Mathematics. Friedr. Vieweg & Sohn, Germany (1987).
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. arithmetic varieties; Arakelov theory; finiteness theorem; Diophantine approximation; transcendental numbers L. SZPIRO , Sur les solutions d'un système d'équations polynomiales sur une variété abélienne (d'après G. FALTINGS and P. VOJTA ) (Séminaire N. Bourbaki, No. 729, June 1990 ). Numdam | Zbl 0746.14010
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. cohomological Hilbert-function; coherent sheaf; vanishing theorem; invariants of a sheaf; linear subdimension; hyperplane section Brodmann M, A priori bounds of Severi type for cohomological Hilbert function, J. Algebra 155 (1993) 298--324
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. quantum fields in curved spacetime; de Sitter; out of equilibrium quantum field theory
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Calabi-Yau threefold; Picard number; classification; diophantine approximation for integral cubic forms D. R. Heath-Brown and P. M. H. Wilson, Calabi-Yau threefolds with \?>13, Math. Ann. 294 (1992), no. 1, 49 -- 57.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. smoothness for regular local rings; Serre's conjecture on intersection multiplicities; Artin's approximation theorem; Chow groups Dutta, S. P., \textit{A theorem on smoothness-bass-Quillen, Chow groups and intersection multiplicity of Serre}, Trans. Amer. Math. Soc., 352, 1635-1645, (2000)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Brauer groups; curves over local fields; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields D. J. Saltman, ''Correction to: ``Division algebras over \(p\)-adic curves'' [J. Ramanujan Math. Soc. 12 (1997), no. 1, 25-47; MR1462850 (98d:16032)],'' J. Ramanujan Math. Soc., vol. 13, iss. 2, pp. 125-129, 1998.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. towers of function fields; Jacobian; rank of a Jacobian; endomorphisms of Jacobians; function field D. Ulmer and Y.G. Zarhin. Ranks of Jacobians in towers of function fields. Math. Res. Lett., 17:637--645, 2010.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. extension of free pencil; prime characteristic Paoletti R. (1995). Free pencils on divisors. Math. Ann. 303: 109--123
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. singularities in positive characteristic; Milnor number in positive characteristic; singularities of algebroid curves
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine approximation of rational points; toric varieties; universal torsors
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. pre-good point; bad \(d\)-fold points; desingularization; surfaces in 3- space; multiplicity of a singular point; strict transform; good point; monoidal transforms; characteristic
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. function fields; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Elimination result; quantities; equations; solution of a problem; surface of second degree; tangential axes
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Bairstow's symmetric function; algebraic descent; arithmetic descent; diophantine equations; comparison of algebraic norms
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. degeneration theorem for K3-surfaces; characteristic p
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Galois covers; lifting of automorphisms of curves; \(p\)-adic discs; curves over local fields; characteristic \(p\); Witt vectors; Kummer-Artin-Schreier-Witt theory B. Green and M. Matignon, ''Liftings of Galois covers of smooth curves,'' Compositio Math., vol. 113, iss. 3, pp. 237-272, 1998.
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. dynamics of rational maps on projective spaces; canonical height; preperiodic points; generalized Mahler formula; bad reduction; bounds of dynamical systems; phenomena of Shafarevich type in dynamics; dynamics over function field
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. elliptic curves over function fields; explicit computation of \(L\)-functions; BSD conjecture; unbounded ranks; explicit Jacobi sums
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. finite fields; recursive towers of function fields; generating function of the Franel number
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine approximation; Liouville's theorem; Arakelov geometry; Seshadri constant; rational points
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. smooth projective varieties; flag varieties; Miyaoka's semipositivity theorem; cotangent bundle; rational surfaces; divisorial contractions; fibrations; crystalline differential operators; étale fundamental group; semistability; reflexives sheaves; semipositive sheaves; uniruled varieties; Riemann-Hilbert correspondence; stable Higgs bundle; Chern classes; flat connections; Artin's criterion of contractibility; Kodaira dimension; Hirzebruch surface; canonical divisor; surfaces of general type; Barlow's surfaces; del Pezzo surfaces; Fano three-folds
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. formal function along a subspace; implicit differentiation; formal power series; standard basis of a local ideal; resolution of singularities Edward Bierstone and Pierre D. Milman, Standard basis along a Samuel stratum, and implicit differentiation, The Arnoldfest (Toronto, ON, 1997) Fields Inst. Commun., vol. 24, Amer. Math. Soc., Providence, RI, 1999, pp. 81 -- 113.
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ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Diophantine equations over function fields Wang, J.T.-Y., Integral points of projective spaces omitting hyperplanes over function fields of positive characteristic, J. number theory, 77, 2, 336-346, (1999)
0
ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. Wronskian; abc conjecture; function fields Hsia, L. -C.; Wang, J. T. -Y.: The ABC theorem for higher-dimensional function fields. Trans. amer. Math. soc. 356, No. 7, 2871-2887 (2004)
1
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank of tensors; salmon conjecture; secant varieties S. Friedland and E. Gross, \textit{A proof of the set-theoretic version of the salmon conjecture}, J. Algebra, 356 (2012), pp. 374--379.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). fat points; sum of decomposable tensors; tensor rank; secant varieties; Segre varieties Catalisano, M.V., Geramita, A.V., Gimigliano, A.: On the rank of tensors, via secant varieties and fat points, zero-dimensional schemes and applications (Naples, 2000). Queen's Papers in Pure and Appl. Math., vol. 123, pp. 133--147. Queen's University, Kingston (2002)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Waring problem; polynomial decomposition; symmetric rank; symmetric tensors; Veronese varieties; secant varieties Ballico, E; Bernardi, A, Unique decomposition for a polynomial of low rank, Ann Polonici Math, 108, 219-224, (2013)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). number of equations; cohomological dimension; arithmetical rank; determinantal varieties; étale cohomology Bruns, W.; Schwänzl, R., The number of equations defining a determinantal variety, Bull. Lond. Math. Soc., 22, 5, 439-445, (1990)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Chow rank; Chow variety; secant varieties; tensors
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). X-rank; secant varieties; rank of tensor; Terracini's question; partially symmetric tensors; Comon's conjecture Buczyński, J.; Landsberg, J.M.; Ranks of tensors and a generalization of secant varieties; Linear Algebra Appl.: 2013; Volume 438 ,668-689.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). discriminant; Cayley-Hamilton theorem; characteristic functions; commutative operator vessel; commutative \(n\)-tuples of Hilbert space operators; finite rank imaginary parts; Banach space operators; determinantal varieties; Bezoutians Kravitsky, N., Discriminant varieties and discriminant ideals for operator vessels in Banach space, Integral Equations Operator Theory, 23, 4, 441-458, (1995)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). symmetric tensors; secant varieties; Veronese varieties; symmetric rank E. Ballico and A. Bernardi, \textit{Decomposition of homogeneous polynomials with low rank}, Math. Z., 271 (2012), pp. 1141--1149, .
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). symmetric tensors; symmetric rank; symmetric border rank; secant varieties to Veronese varieties Bernardi, A.; Gimigliano, A.; Idà, M., Computing symmetric rank for symmetric tensors, J. Symb. Comput., 46, 1, 34-53, (2011)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). \(t\)-minors; \(t\)-Pfaffians; determinantal varieties; arithmetical rank; ASL; cohomological dimension; De Rham cohomology Barile M.,Arithmetical ranks of ideals associated to symmetric and alternating matrices, J. Algebra,176 (1995), 59--82.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). singular value decomposition; tensors; singular space of a tensor; best rank \(r\) approximation; secant varieties; tangent space; critical points; Euclidean distance degree G. Ottaviani, R. Paoletti, A geometric perspective on the singular value decomposition. \textit{Rend. Istit. Mat. Univ. Trieste}\textbf{47} (2015), 107-125. MR3456581 Zbl 1345.15006
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). textbook (algebraic geometry); schemes and morphisms; prevarieties; quasi-coherent sheaves; vector bundles; divisors; algebraic curves; determinantal varieties; singularities Görtz, U., Wedhorn, T.: Algebraic Geometry I. Vieweg+Teubner, Wiesbaden (2010)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; minimal submanifolds; singular value decomposition; symmetric matrices with repeated eigenvalues
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). bitangent; dual of projective varieties; characteristic 2; ordinary varieties; rank of a projective variety Ballico E.: On the dual of projective varieties. Canad. Math. Bull. 34, 433--439 (1991)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). rank 2 bundles; moduli of stable bundles; rational varieties
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). 2-adic valuations of ratio of products of factorials; parity of degrees of determinantal varieties; subspaces of real skew symmetric matrices; subspaces of real rectangular matrices; parity of number of plane partitions; parity of number of symplectic tableaux Beauville, A.: Surfaces algébriques complexes, Astérisque 54, Soc. Math. de France (1978)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). maximum likelihood; duality; determinantal varieties; matrices J. Draisma and E. Horobeţ: \textit{The average number of critical rank-one approximations to a tensor}, arxiv:1408.3507.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). 2-linear resolutions; syzygies; depth; cohomological dimensions; arithmetical rank; scrolls; linearly joined varieties; monomial ideals Morales, M, Simplicial ideals, 2-linear ideals and arithmetical rank, J. Algebra, 324, 3431-3456, (2010)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). group schemes; support varieties; rank varieties; \(p\)-points; thick subcategories; stable module categories; cohomology rings; finite-dimensional cocommutative Hopf algebras Friedlander, E. M.; Pevtsova, J., \({\Pi}\)-supports for modules for finite group schemes, Duke Math. J., 139, 2, 317-368, (2007)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). symmetric tensors; spectral norm; rank-one approximation; rank-two tensors
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal variety; classification of Cremona transformations; systems of quadrics through Severi varieties; quintic elliptic scroll Ein L. and Shepherd-Barron N., Some special Cremona transformations, Amer. J. Math. 111 (1989), 783-800.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tensor rank; homotopy continuation; numerical elimination theory; numerical algebraic geometry; joins; secant varieties; numerical examples Bernardi, A.; Daleo, NS; Hauenstein, JD; Mourrain, B., Tensor decomposition and homotopy continuation, Differential Geom. Appl., 55, 78-105, (2017)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). derived category; semi-orthogonal decompositions; projective varieties; determinantal varieties; homological projective duality; rationality questions M. Bernardara, M. Bolognesi and D. Faenzi, Homological projective duality for determinantal varieties, preprint (2014), .
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). moduli space of rank \(r\) stable vector bundles; Grassmannian; flag varieties Ballico, E.; Ramella, L., The restricted tangent bundle of smooth curves in grassmanians and curves in flag varieties, Rocky Mountain J. Math., 30, 1207-1227, (2000)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). family of abelian varieties; large Mordell-Weil rank; elliptic curve F. Hazama, The Mordell-Weil group of certain abelian varieties defined over the rational function field,Tohoku Math. J. 44 (1992), 335--344.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). geometric invariant theory; connected reductive group; maximal unipotent subgroup; complexity; minimal codimension; rank; actions on affine varieties; Poincaré series; simple Lie algebra D. I. Panyushev, Complexity and rank of actions in invariant theory,'' J. Math. Sci. (New York), 95, No. 1, 1925--1985 (1999).
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). textbook (algebraic geometry); schemes and morphisms; prevarieties; quasi-coherent sheaves; vector bundles; divisors; algebraic curves; determinantal varieties; singularities
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal ideals and varieties Tomaž Košir and B. A. Sethuraman, A Groebner basis for the 2\times 2 determinantal ideal \mod\?², J. Algebra 292 (2005), no. 1, 138 -- 153.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). invariant theory; null cone; orbit closure; multi-determinantal algebraic varieties; algebraic varieties; singular matrices; vanishing ideal
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). abelian varieties; exponential map; Kummer theory; categoricity; Morley rank
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Stanley-Reisner ring; straightening law; standard bitableaux; Abhyankar formula; Hilbert polynomial; determinantal ideals; nonintersecting lattice paths; Hilbert series; Hilbert function; Schubert varieties DOI: 10.1016/0378-3758(95)00156-5
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). K-theory of endomorphisms; determinantal varieties; ring of the big Witt vectors Michiel Hazewinkel, Operations in the \?-theory of endomorphisms, J. Algebra 84 (1983), no. 2, 285 -- 304.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). syzygies; determinantal varieties; permanents; general linear superalgebra Raicu, C., Weyman, J.: The syzygies of some thickenings of determinantal varieties. arXiv:1411.0151v1
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Stanley-Reisner rings; Gröbner bases; determinantal varieties; first-order jet schemes Boyan Jonov, Shellability of a complex associated to the first order jet scheme of a determinantal variety, in preparation.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Fano varieties; Mori fibre spaces; toric varieties; vertex-transitive polytopes; high index; high Picard rank
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). mixed ladder determinantal varieties; Schubert varieties Gonciulea, N.; Miller, C., Mixed ladder determinantal varieties, \textit{J. Algebra}, 231, 1, 104-137, (2000)
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Segre products; secant varieties; Gröbner bases; secant ideals; tensors
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). Fano schemes; determinantal varieties; permanent M. Chan and N. Ilten, \textit{Fano schemes of determinants and permanents}, Algebra Number Theory, 9 (2015), pp. 629--679, .
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). vector bundles; Hilbert schemes; determinantal varieties Hideyasu Sumihiro, Determinantal varieties associated to rank two vector bundles on projective spaces and splitting theorems, Hiroshima Math. J. 29 (1999), no. 2, 371 -- 434.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). widerank; open rank; symmetric tensor rank; reducible varieties; lines; strange variety
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). nonnegative tensors; nonnegative tensor rank; nonnegative typical ranks; best nonnegative rank-\(r\) approximations; semialgebraic geometry; uniqueness and identifiability Y. Qi, P. Comon, and L.-H. Lim, \textit{Semialgebraic geometry of nonnegative tensor rank}, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 1556--1580, .
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). abelian varieties; isogenies; Tate modules; locally free modules of rank 1
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). tensor rank; border tank: infinite-dimensional tensors J. Draisma and J. Kuttler, Bounded-rank tensors are defined in bounded degree, Duke Math. J. 163 (2014), no. 1, 35-63.
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). degeneracy loci; Chow groups; Chern numbers of determinantal varieties; resultant P. PRAGACZ , Determinantal Varieties and Symmetric Polynomials (Functional Analysis and Its Applications, Vol. 21, N^\circ 3, pp. 89-90, 1987 ). MR 90h:14072a | Zbl 0633.14029
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). determinantal varieties; codimension; degree
0
rank varieties; determinantal varieties; skewsymmetric tensors O. Porras, ''Rank varieties and their desingularizations,''J. Algebra,186, 677--723 (1996). symmetric tensors; tensor decomposition; Waring rank; tangential rank; cactus rank; algorithms
0