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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) \(\lambda\)-connection; moduli space; Picard group; algebraic function; automorphism
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Castelnuovo inequality; minimal algebraic surface of general type; Veronese surface; rational normal scroll; canonical model; deformations; number of moduli; pencil of nonhyperelliptic curves Ashikaga, T.; Konno, K., Algebraic surfaces of general type with \(c_1^2 = 3 p_g - 7\), Tohoku Math. J., 42, 517-536, (1990)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic surface; diametrical surface; polar surface; asymptotic direction; invariant group; reflections
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real algebraic variety; Hilbert's 16th problem; topology of real algebraic curves; curves on ellipsoid
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Chow group; Bloch's conjecture; Godeaux surface; algebraic cycles Voisin, Claire, Sur les zéro-cycles de certaines hypersurfaces munies d'un automorphisme, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 19, 4, 473-492, (1992)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) lifting problem; deformation of \({\mathbb{G}}_ a\) to \({\mathbb{G}}_ m\); characteristic p; automorphism group; Galois covering of curves; class field theory; Artin-Schreier sequence; Kummer sequence Sekiguchi, T.; Oort, F.; Suwa, N., On the deformation of Artin-Schreier to Kummer, Annales Scientifiques de l'École Normale Supérieure, 22, 345-375, (1989)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) cubic threefolds; intermediate Jacobian; elliptic curves; abelian surface with real multiplication van Geemen, B., Yamauchi, T.: On intermediate Jacobians of cubic threefolds admitting an automorphism of order five, to appear in the Looijenga volume of the Pure and Applied Math Quarterly
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) plane algebraic curves; filtred algebras; Rees algebras; Riemann-Roch theorem; genus; curve singularities E.KUNZ,Introduction to Plane Algebraic Curves, Birkh''auser Boston, Inc., Boston, MA, 2005. Translated from the 1991 German edition by Richard G. Belshoff.MR2156630
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic K3 surfaces; Néron-Severi group; finite generation of; automorphism group; finite number of orbits; reduction theory Sterk H.: Finiteness results for algebraic K3 surfaces. Math. Z. 189, 507--513 (1985)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Azumaya algebras; Brauer groups; Brauer-Manin obstructions; Hasse principle; quartic curves; curves of genus 1; Tate-Shafarevich group DOI: 10.1007/s00605-012-0387-8
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) classification of algebraic curves; bound for the arithmetic genus
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) complex conjugation; number of connected components; symmetric surfaces; real plane curves; genus; separating number
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic function field; automorphism group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) log pair; Fano-type surface; automorphism group; torus action; fundamental group of the smooth locus; klt 3-fold singularity
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) gluing of charts; topology of curves; Viro method; real algebraic varieties; Newton polyhedra; pseudo-holomorphic curves Itenberg I., Shustin E. (2002). Combinatorial patchworking of real pseudo-holomorphic curves. Turkish J. Math. 26(1): 27--51
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) complex elliptic curve as real algebraic surface Bochnak, J., Huisman, J.: When is a complex elliptic curve the product of two real algebraic curves? Math. Ann.293 (1992)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) field of moduli of a closed Riemann surface; Riemann surfaces of genus three; conformal automorphism
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Kummer surface; Brauer group; rational points; torsion of elliptic curves A.N. Skorobogatov, Yu.G. Zarhin, The Brauer group of Kummer surfaces and torsion of elliptic curves, J. Reine Angew. Math. 666, 115-140 (2012)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) braid group; diffeomorphisms; algebraic variety; pure braid; hyperbolic closure; link; fibres; Gassner representation; pure braid group; lower central series; fundamental group; parallel incompressible surface DOI: 10.2307/2374725
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) reconstruction theorem; abelian category; noncommutative algebraic geometry; quasi-coherent sheaves; automorphism class group; quasi-separated scheme; the spectrum of $\mathcal A$; equivalence of groupoids; automorphism class group; derived category of coherent sheaves; tensor triangulated category of perfect complexes; Tannaka duality
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic curves; rational curves; parameterization methods; envelope curves; genus
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real Schubert calculus; Wronski map; rational normal curves; characters of the symmetric group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Riemann surface; automorphism group; Fuchsian group Costa, A. F.; Izquierdo, M., One-dimensional families of Riemann surfaces of genus \textit{g} with \(4 g + 4\) automorphims, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., (2018)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Hilbert modular variety; unit with negative norm; cyclotomic fields; cyclic fields; Hilbert modular group; arithmetical genus; number of elliptic fixed points; class number; totally real fields Keqin, F.: On arithmetic genus of Hilbert modular varieties on cyclic number fields. Sci. China 27, 576-584 (1984)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) rational points on algebraic curves; genus
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic curve; canonical ideal; automorphism group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real abelian varieties; real structures on complex varieties; real curves; compact Riemann surface Ciro Ciliberto and Claudio Pedrini, Real abelian varieties and real algebraic curves, Lectures in real geometry (Madrid, 1994) De Gruyter Exp. Math., vol. 23, de Gruyter, Berlin, 1996, pp. 167 -- 256.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) curves of genus three; real multiplication; abelian variety Hoffman, J. W.; Wang, H.: 7-gons and genus 3 hyperelliptic curves. Rev. R. Acad. cienc. Exactas fís. Nat., ser. A mat. 107, 35-52 (2013)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) hyperelliptic curve; automorphism of compact Riemann surface; Fuchsian group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Betti number of an abelian covering of a \(CW\)-complex; cyclotomic coordinates; fundamental group; complement to an algebraic curve; link; Alexander polynomials of plane algebraic curves Libgober A.: On the homology of finite abelian coverings. Topol. Appl. 43(2), 157--166 (1992)
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) weighted complete intersection; automorphism group; linear algebraic group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) two-dimensional topological quantum field theory; quantum cohomology; symplectic manifolds; algebraic curves; moduli of algebraic curves; higher-genus symplectic invariants; topological gravity Pandharipande R, Pixton A, Zvonkine D. Relations on \(\mathcal{M}\=\)\_{}\{g,n\} via 3-spin structures. ArXiv:1303.1043
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) finite field; finite subgroup; algebraic group; automorphism; fixed point; Smith theory Serre, J.P.: How to use finite fields for problems concerning infinite fields. In: Arithmetic, Geometry, Cryptography and Coding Theory, Volume 487 of Contemporary Mathematics, pp. 183-193. American Mathematical Society, Providence, RI (2009)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) plane algebraic curves; field of characteristic zero; automorphism groups; Fermat curve; Riemann surfaces
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) \(K3\) surface; automorphism group; nef cone; fundamental domain
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real algebraic geometry; computational geometry; geometric modeling; plane curves; singularities; visualization; algorithms; benchmarks; challenges Labs, O.: A list of challenges for real algebraic plane curve visualization software, The IMA volumes in mathematics and its applications 151, 137-164 (2010)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) hyperelliptic curves; AG codes; Riemann-Roch spaces; \(SL(2,p)\) representations; automorphism group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) wonderful compactification; automorphism group; simple algebraic group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) semisimple algebraic groups; parabolic subgroups; connected linear algebraic group; parabolic factorizations; automorphism group A. L. Oniščik, Parabolic factorizations of semisimple algebraic groups, Math. Nachr. 104 (1981), 315 -- 329.
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Deligne-Lusztig curves; maximal curve; automorphism group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) points in general position; generic rational surface; biregular automorphism group Koitabashi M., Automorphism groups of generic rational surfaces, J. Algebra, 1988, 116(1), 130--142
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) SUSY algebraic curves; quantum supergroups; quantum general linear group; Hopf superalgebra; Flag superspaces; Schubert supercells Manin, Y. I. 1991. ''Topics in Noncommutative Geometry''. Princeton Univ. Press.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) \(L\)-function; Shimura variety; Hilbert-Blumenthal surface; Tate's conjectures for abelian fields; group of algebraic cycles; intersection cohomology; canonical intermediate-perversity extension; Hirzebruch- Zagier cycles; Tate class Gordon, B. B.: Algebraic cycles in families of abelian varieties over Hilbert -- blumenthal surfaces. J. reine angew. Math. 449, 149-171 (1994)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) reductive algebraic group; categorical quotient; adjoint representation; automorphism; Luna stratification
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) symmetric space; homogeneous varieties; algebraic curves; genus 9; \(K3\) surfaces Mukai, S.: Curves and symmetric spaces, II. Ann. Math. (2) \textbf{172}(3), 1539-1558 (2010)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) degree 2 coverings; real forms of algebraic curves Bujalance, E., Conder, M., Gamboa, J.M., Gromadzki, G., Izquierdo, M.: Double coverings of Klein surfaces by a given Riemann surface. J. Pure Appl. Algebra 169(2--3), 137--151 (2002)
1
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real algebraic \(K3\)-surface; real algebraic cycles; moduli space; Kähler surface Frédéric Mangolte, Cycles algébriques sur les surfaces \?3 réelles, Math. Z. 225 (1997), no. 4, 559 -- 576 (French).
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) non-commutative surface; noncommutative bundle; intersection theory; Grothendieck group; noncommutative algebraic geometry I. Mori, and, S. P. Smith, The Grothendieck group of a quantum projective space bundle, submitted.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic surface; diametrical surface; polar surface; asymptotic direction; invariant group; reflections
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) moduli space of complex isomorphism classes of real algebraic curves; semialgebraic varieties Seppälä, M, Real algebraic curves in the moduli space of complex curves, Compositio Math., 74, 259-283, (1990)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) covering of stable genus three curves; fibre of Prym map; abelian surface; symmetric theta divisor; Satake compactification of the moduli space of principally polarized abelian surfaces Verra, A.: The fiber of the Prym map in genus 3. Math. Ann. 276, 433--448 (1987)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) automorphism group; linear algebraic group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) \(K3\) surface; degeneration; Picard lattice; automorphism group
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) linear series; real algebraic curves; Wronskians
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) hyperelliptic curves; automorphism group; dihedral invariants Shaska, T.: Computational aspects of hyperelliptic curves, Computer mathematics. In: Proceedings of the sixth Asian symposium (ASCM 2003), Beijing, China, April 17--19, 2003. World Scientific. River Edge Lect. Notes Ser. Comput. 10, 248--257 (2003)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) classifying projective algebraic surfaces with low sectional genus; rational surface; adjunction mapping Biancofiore, A., Livorni, E.: On the Iteration of the Adjunction Process in the Study of Rational Surfaces. Indiana Math. J.36 (no. 1), 167--188 (1987)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) plane curves; divisor on algebraic surface; local trees; weighted graph; desingulariztion Daigle, D.: Local trees in the theory of affine plane curves, J. math. Kyoto univ. 31, 593-694 (1991)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Diophantine theory of genus 1 curves; local-global principle; rational points; heights; finite basis theorem; Tate-Shafarevich group; arithmetic of elliptic curves J.W.S. Cassels, \textit{Lectures on elliptic curves}, \textit{Lond. Math. Soc. Stud. Texts}\textbf{24}, Cambridge University Press, Cambridge, U.K., (1991).
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Quotients of products of curves; Beauville surface; Beauville structure; simple group; quasi-simple group Y. Fuertes and G.\ A. Jones, Beauville surfaces and finite groups, J. Algebra 340 (2011), 13-27.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Xiao's conjecture; algebraic surface; birational geometry; canonical fibration; family of curves
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) abelian surface; singluarities of curves; curves of low genus; isogeny; Jacobian variety; nonprimitive polarization
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) genus of a Riemann surface; generalised Castelnuovo curves; linear series
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) numerical examples; toric surfaces; singular curves; rational curves; algorithm; rational parametrization; plane algebraic curves of genus zero; Newton polygon Beck, T.; Schicho, J., Curve parametrization over optimal field extensions exploiting the Newton polygon, (), 119-140
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) singularity; rational curve; algebraic surface; Chern numbers; elliptic curves F. HIRZEBRUCH , On the characteristic classes of differentiable manifolds (Colloque H. Poincaré, octobre 1954 ).
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Riemann surface; algebraic curve; Hurwitz curve; automorphism; Jacobians
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) \(K3\) surface; symplectic automorphism; Mathieu group; Niemeier lattice; Leech lattice
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic curves; positive characteristic; automorphism groups
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) generic morphism; branch curve; discriminant curve; Chisini's conjecture; surface of general type; braid monodromy; cuspidal algebraic curves Kulikov S.\ V. and Teicher M., Braid monodromy factorizations and diffeomorphism types, Izv. Ross. Akad. Nauk Ser. Mat. 64 (2000), no. 2, 89-120.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic curves; finite fields; automorphism groups
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic group; \(G\)-bundles over elliptic curves Friedman, R.; Morgan, JW; Witten, E., Principal \(G\)-bundles over elliptic curves, Math. Res. Lett., 5, 97-118, (1998)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) geometric complexity; cellular spaces; order relation; curves; knots and links; real algebraic geometry
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Diophantine approximation; rational points on algebraic varieties; arithmetic algebraic geometry; Roth's theorem; nonvanishing lemma for polynomials in several variables; Roth's lemma; Dyson's lemma; Mordell conjecture; Faltings' theorem; finiteness of rational points; algebraic curve of genus greater than one; Vojta's generalization of Dyson's lemma; products of curves of arbitrary genus; Lang conjecture; Subspace Theorem; lower bound for the rational approximation to a hyperplane
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) L\({}^ 2\)-arithmetic genus; algebraic curves; (partial d)-bar-operator; resolution of singularities Brüning, J.; Peyerimhoff, N.; Schröder, H., The \(\overline{\partial }\)-operator on algebraic curves, Commun. Math. Phys., 129, 525-534, (1990)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Schottky uniformization of algebraic curves; real hyperelliptic \(M\)-curves; Schottky-Klein prime function; explicit conformal slit mapping
0
automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) generalized Wallach space; Einstein metric; Ricci flow; planar dynamical system; singular point; real algebraic surface Abiev, N.A., Arvanitoyeorgos, A., Nikonorov, Y.G., Siasos, P.: The dynamics of the Ricci flow on generalized Wallach spaces. Differ. Geom. Appl. \textbf{35}(Suppl.), 26-43 (2014)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) infinitely near points; algebraic group actions; field of invariant rational functions; rationality of moduli spaces of pointed plane curves Mazouni, A, Quotient de la variété des points infiniment voisins d'ordre 9 sous l'action de \(PGL_{3}\), Bull. SMF, 124, 425-455, (1996)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Klein surfaces; finite group actions; full real genus
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic curves; positive characteristic; automorphism groups Giulietti, M.; Korchmáros, G., Algebraic curves with many automorphisms
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) position of algebraic curves; real curves; ovals; Thom conjecture
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) spectrahedron; \(K3\)-surface; real quartic surface; singular quartic surface; convex algebraic geometry; transversal determinantal quartic Degtyarev, A.; Itenberg, I., On real determinantal quartics, (Proceedings of the Gökova geometry-topology conference 2010, (2011), Int. Press Somerville, MA), 110-128
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic stability; branched cover; moduli space of genus zero curves; Hurwitz space; dynamical degree
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) compact Riemann surface; automorphism group; metacyclic group; \(Z\)-group; cyclic Sylow subgroup; group of square-free order; exponent Schweizer, A.: Metacyclic groups as automorphism groups of compact Riemann surfaces. https://doi.org/10.1007/s10711-017-0239-8\textbf{(to appear in Geom Dedicata)}
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) curves of genus three; real multiplications; abelian variety
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) moduli stack; one point marked smooth projective curves of genus; Galois-Teichmüller modular group Hiroaki Nakamura, Galois representations in the profinite Teichmüller modular groups, Geometric Galois actions, 1, London Math. Soc. Lecture Note Ser., vol. 242, Cambridge Univ. Press, Cambridge, 1997, pp. 159 -- 173.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) coverings; Grothendieck theory; dessin d'enfant; theorem of Belyi; automorphism; algebraic curves Jean-Marc Couveignes. À propos du théorème de Belyi.Journal de théorie des nombres de Bordeaux, 8:93--99, 1996.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) real trigonal curves; rigid isotopy; Hirzebruch surface Zvonilov, VI, Isotopies of real trigonal curves on Hirzebruch surfaces, J. Math. Sci., 113, 804-809, (2003)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) connected reductive linear algebraic group; automorphism; symmetric variety; Borel subgroup; double cosets; B-orbits; action; Zariski closure; Bruhat order Richardson-Springer R. W. Richardson and T. A. Springer: The Bruhat order on symmetric varieties. Geom. Dedicata \textbf 35 (1990), 389--436.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) elliptic genus; formal group laws associated to supersingular elliptic curves G. Teodosiu, A class of analytic coverings ramified over \(u^3=v^2\), J. London Math. Soc. (2) 38 (1988), 231-242. Zbl0619.14009 MR966295
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) elliptic curve over the rational function field; ring of invariants; excellent families of elliptic curves; Weyl group; Mordell-Weil lattice of a rational elliptic surface Shioda, T; Usui, H, Fundamental invariants of Weyl groups and excellent families of elliptic curves, Comment. Math. Univ. St. Pauli, 41, 169-217, (1992)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912).
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Theta functions; Abelian integrals; periods; Riemann surface; algebraic curves; characteristics; transformation theory.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) tachyon scattering amplitudes; divisiors with complex coefficients; moduli space of complex algebraic curves of genus \(g\) with \(n\) given points; Belavin-Knizhnik theorem; bosonic string theory; Polyakov volume form; Weil-Deligne pairings; Arakelov measures; Quillen metrics
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Jacobian; period matrices; hyperelliptic curves with reduced automorphism group Schindler B, Period matrices of hyperelliptic curves, Manuscripta. Math. 78 (1993) 369--380
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Lie group with compatible real algebraic structure; locally Nash group; algebraic addition theorem; semialgebraic groups [M-S] J. Madden and C. Stanton,One dimensional Nash groups, Pacific J. Math.154 (1992), 331--344.
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Riemann surface; automorphism group; Hurwitz group Schweizer, A, On the exponent of the automorphism group of a compact Riemann surface, Arch. Math. (Basel), 107, 329-340, (2016)
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) algebraic cycles; Chow group; motive; Bloch-Beilinson filtration; surface of general type; \(K3\) surface; Beauville's ``splitting property'' conjecture; multiplicative Chow-Künneth decomposition
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) optimal curve; algebraic-geometric code; function field; automorphism group of AG-code
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) automorphism group; Severi-Brauer surface; cyclic algebra
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automorphism group; genus 2 surface; real algebraic curves Cirre F.J.: Complex automorphism groups of real algebraic curves of genus 2. J. Pure Appl. Algebra 157(2--3), 157--181 (2001) Thetanullwerte; analog radar signal design; radar synthesis; invariance problem for radar ambiguity surfaces; symplectic time-frequency plane; radar auto-ambiguity functions; positive definiteness; symplectic form; linear oscillator representation; metaplectic group; Computer Aided Geometric Design; ambiguity surface preservation principle; coaxial optical systems; Whittaker-Shannon-Kotel'nikov sampling theorem; digital signal processing; nilpotent harmonic analysis; linear Schrödinger representation; real Heisenberg group; Laguerre functions; theta- identities; theta-null values; nilpotent Lie group; Maslov-Souriau index Schempp, W.: Analog radar signal design and digital signal processing--A Heisenberg nilpotent Lie group approach. Lecture notes in physics 250, 1-27 (1986)
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