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HD 109749-Planetary system-In 2005, an exoplanet was discovered around HD 109749 A. It was detected by the radial velocity method as part of the N2K Consortium. It is a hot Jupiter with a minimum mass of 0.28 MJ and a semimajor axis of 0.06 AU. | milkshake721/2.1M-wiki-STEM |
Orbit Downloader-Orbit Downloader-Orbit Downloader is a discontinued download manager for Microsoft Windows. Launched in 2006, its developers abandoned it in 2009. In 2013, Orbit Downloader was classified as malware by antivirus software after ESET discovered a botnet in the application. | milkshake721/2.1M-wiki-STEM |
Orbit Downloader-Features-One of the main features of the program is its ability to grab and download embedded Flash Video files from online video platforms. Orbit Downloader also accelerates downloads by acting as a peer-to-peer client, utilizing bandwidth of other users.
Orbit Downloader supports downloading from HTT... | milkshake721/2.1M-wiki-STEM |
Orbit Downloader-Funding and malicious conduct-Although Orbit Downloader is free, it is an advertising-supported product since it offers to change the web browser's homepage upon installation and also offers to install software that are not critical for its operation. Also it has begun to display built-in ads inside th... | milkshake721/2.1M-wiki-STEM |
Paced Auditory Serial Addition Test-Paced Auditory Serial Addition Test-Paced Auditory Serial Addition Test (PASAT) is a neuropsychological test used to assess capacity and rate of information processing and sustained and divided attention.Originally the test was known as the Paced Auditory Serial Addition Task (PASAT)... | milkshake721/2.1M-wiki-STEM |
Paced Auditory Serial Addition Test-Multiple sclerosis-It has become widely used in the testing of patients with multiple sclerosis as patients with this disease frequently have an impaired performance on this test. The PASAT was included in the Multiple Sclerosis Functional Composite as a cognitive measure. However, t... | milkshake721/2.1M-wiki-STEM |
Apocrine-Apocrine-Apocrine () glands are a type of exocrine gland, which are themselves a type of gland, i.e. a group of cells specialized for the release of secretions. Exocrine glands secrete by one of three means: holocrine, merocrine and apocrine. In apocrine secretion, secretory cells accumulate material at their ... | milkshake721/2.1M-wiki-STEM |
Apocrine-Apocrine-An example of true apocrine glands is the mammary glands, responsible for secreting breast milk. Apocrine glands are also found in the anogenital region and axillae.Apocrine secretion is less damaging to the gland than holocrine secretion (which destroys a cell) but more damaging than merocrine secret... | milkshake721/2.1M-wiki-STEM |
Apocrine-Apocrine metaplasia-Apocrine metaplasia is a reversible transformation of cells to an apocrine phenotype. It is common in the breast in the context of fibrocystic change. It is seen in women mostly over the age of 50 years. Metaplasia happens when there is an irritation to the breast (breast cyst). Apocrine-li... | milkshake721/2.1M-wiki-STEM |
Apocrine-Apocrine ductal carcinoma in situ-Apocrine ductal carcinoma in situ (ACDIS) is a very rare breast carcinoma which is regarded as a variant of the ductal carcinoma in situ breast tumors. ACDIS tumors have microscopic histopathology features that are similar to pure apocrine carcinoma of the breast tumors but di... | milkshake721/2.1M-wiki-STEM |
Apocrine-Apocrine carcinoma-Apocrine carcinoma is a very rare form of female breast cancer. The rate of incidence varies from 0.5 to 4%. Cytologically, the cells of apocrine carcinoma are relatively large, granular, and it has a prominent eosinophilic cytoplasm. When apocrine carcinoma is tested as a “triple negative",... | milkshake721/2.1M-wiki-STEM |
Oral and maxillofacial radiology-Oral and maxillofacial radiology-Oral and maxillofacial radiology, also known as dental and maxillofacial radiology, is the specialty of dentistry concerned with performance and interpretation of diagnostic imaging used for examining the craniofacial, dental and adjacent structures.Oral... | milkshake721/2.1M-wiki-STEM |
Oral and maxillofacial radiology-Training-United States Oral or dental maxillofacial radiology is one of nine dental specialties recognized by the American Dental Association.To become an oral and maxillofacial radiologist one must first complete a dental degree and then apply for and complete a postgraduate course of ... | milkshake721/2.1M-wiki-STEM |
Oral and maxillofacial radiology-Training-The Commission on Dental Accreditation accredited programs are a minimum of two years in length. Several accredited programs in oral maxillofacial radiology require the resident to complete a master's degree, whereas others allow the option of pursuing a concurrent PhD or maste... | milkshake721/2.1M-wiki-STEM |
Oral and maxillofacial radiology-Training-Australia Australian programs are accredited by the Australian Dental Council and are 3 years in length, culminating in either a master's degree (MDS or MPhil) or a Doctor of Clinical Dentistry degree (DClinDent). Currently, the only Australian institution offering specialist t... | milkshake721/2.1M-wiki-STEM |
Oral and maxillofacial radiology-Training-Fellowship can then be acquired through the Royal Australia New Zealand College of Radiologists and/or the Royal Australasian College of Dental Surgeons. Oral and maxillofacial radiologists in Australia tend to work in the private sector, reporting in medical radiology practice... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Glossary of classical algebraic geometry-The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century,... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Glossary of classical algebraic geometry-Dolgachev (2012) translates many of the classical terms in algebraic geometry into scheme-theoretic terminology. Other books defining some of the classical terminology include Baker (1922a, 1922b, 1923, 1925, 1933a, 1933b), Coolidge (1931... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Conventions-The change in terminology from around 1948 to 1960 is not the only difficulty in understanding classical algebraic geometry. There was also a lot of background knowledge and assumptions, much of which has now changed. This section lists some of these changes.
In clas... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Conventions-Definitions in classical algebraic geometry were often somewhat vague, and it is futile to try to find the precise meaning of some of the older terms because many of them never had a precise meaning. In practice this did not matter much when the terms were only used ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Conventions-Algebraic geometry was often implicitly done over the complex numbers (or sometimes the real numbers).
Readers were often assumed to know classical (or synthetic) projective geometry, and in particular to have a thorough knowledge of conics, and authors would use ter... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Conventions-Several terms, such as "Abelian group", "complete", "complex", "flat", "harmonic", "homology", "monoid", "normal", "pole", "regular", now have meanings that are unrelated to their original meanings. Other terms, such as "circle", have their meanings tacitly changed t... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Conventions-Sometimes capital letters are tacitly understood to stand for points, and small letters for lines or curves. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Symbols-[1], [2], . . . , [n] Projective space of dimension 1,2,…,n . This notation was introduced by Schubert (1886).
∞¹, ∞², ...
A family of dimension 1, 2, ...
{1}, {2}, ...,{n} A family or variety of dimension 1,2,…,n . (Semple & Roth 1949, p.288) | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-Abelian group 1. An archaic name for the symplectic group.
2. A commutative group.
aberrancy The deviation of a curve from circular form. See Salmon (1879, p. 356). | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-absolute 1. A fixed choice of something in projective space, used to construct some other geometry from projective geometry. For example, choosing a plane, called the absolute plane, of projective space can be used to make its complement into a copy of affine space. Choosing a... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-2. Absolute geometry is roughly Euclidean geometry without the parallel postulate.
accidental An accidental (or improper) double point of a surface in 4-dimensional projective space is a double point with two distinct tangent planes. (Baker 1933b, vol 6, p. 157) acnode An acn... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-adjoint If C is a curve, an adjoint of C is a curve such that any point of C of multiplicity r has multiplicity at least r–1 on the adjoint. Sometimes the multiple points of C are required to be ordinary, and if theis condition is not satisfied the term "sub-adjoint" is used. ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-2. An affine variety is a variety in affine space.
affinity An automorphism of affine space.
aggregate A set.
ambient An ambient variety is a large variety containing all the points, curves, divisors, and so on that one is interested in.
anharmonic ratio Cross-ratio antipoint ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-Aronhold set One of the 288 sets of 7 of the 28 bitangents of a quartic curve corresponding to the 7 odd theta characteristics of a normal set. associated 1. An associated curve is the image of a projective curve in a Grassmannian, given by taking the tangent lines, or oscula... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-A-azygetic Unpaired. Opposite of syzygetic, meaning paired. Example: azygetic triad, azygetic tetrad, azygetic set. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-B-base 1. A base point is a point common to all members of a family.
2. The base number ρ is the rank of the Neron–Severi group.
bicircular Having nodes at the two circular points at infinity, as in bicircular curve. See Salmon (1879, p.231).
bicorn A bicorn is a curve with two ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-B-bifid 1. Split into two equal parts 2. A bifid map is an element of the vector space of dimension 2g over the field with 2 elements, consisting of the 2g+1-dimensional space of even-cardinality subsets of a set S of 2+2g elements, modulo the 1-dimensional space {0,S}. (Dolgach... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-B-biflecnode Same as fleflecnode. See Salmon (1879, p.210).
bigenus The second plurigenus P2 of a surface.
bihomogeneous Homogeneous in each of two sets of variables, as in bihomogeneous form.
binary Depending on two variables, as in binary form binodal Having two nodes binode A... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-B-bipunctual 1. Having two points 2. For a bipunctual conic with respect to 3 points see Baker (1922b, vol 2, p. 123). birational 1. Two varieties are birational if they are isomorphic off lower-dimensional subsets 2. A birational map is a rational map with rational "inverse" b... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-B-biscribed Both circumscribed and inscribed, or in other words having vertices that lie on a curve and sides that are tangent to the curve, as in biscribed triangle. (Dolgachev 2012) bitangent A bitangent is a line that is tangent to a curve at two points. See Salmon (1879, p. ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-canonical 1. The canonical series is the linear series of the canonical line bundle 2. The canonical bundle is the line bundle of differential forms of highest degree. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-3. The canonical map or canonical embedding is the map to the projective space of the sections of the canonical bundle 4. A canonical curve (or variety) is the image of a curve (or variety) under the canonical map 5. The canonical class is the divisor class of a canonical divi... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-catalecticant A catalecticant is an invariant of a binary form of degree 2n that vanishes when the form is a sum of powers of n linear forms. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-caustic A caustic is the envelope of light rays from a point reflected in a curve Cayley Cayleyan Named after Arthur Cayley 1. See Salmon (1879) 2. A Cayley octad is a set of 8 points in projective space given by the intersection of three quadrics. (Dolgachev 2012, 6.3.1) 3. ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-4. A Cayley absolute is a conic or quadric used to define a metric. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-center centre 1. A special point associated with some geometric object 2. The center of a perspectivity 3. The center of an isologue character characteristic 1. An integer associated with a projective variety, such as its degree, rank, order, class, type. (Semple & Roth 1949, ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-chord A line joining two points of a variety chordal variety A chordal variety is the union of the chords and tangent spaces of a projective variety circle A plane conic passing through the circular points at infinity. For real projective geometry this is much the same as a ci... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-circumscribed 1. Having edges tangent to some curve, as in circumscribed quadrilateral.
2. Passing through the vertices of something, as in circumscribed circle.
cissoid A cissoid is the curve generated from two curves and a point. See Salmon (1879). | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-class 1. The class of a plane curve is the number of proper tangents passing through a generic point of the plane. (Semple & Roth 1949, p.28) 2. The class of a space curve is the number of osculating planes passing through a generic point of space. (Semple & Roth 1949, p.85) 3... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-coaxal coaxial A pencil of circles is called coaxal if their centers all lie on a line (called the axis). | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-A family of plane circles all passing through the same two points (other than the circular points at infinity). (Baker 1922b, vol 2, p. 66) coincidence 1. A coincidence quadric is a quadric associated to a correlation, given by the locus of points lying in the corresponding h... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-complete 1. A linear series of divisors is called complete if it is not contained in a larger linear series.(Semple & Roth 1949, p.351) 2. A scheme is called complete if the map to a point is proper 3. A complete quadrangle is 4 points and the 6 lines joining pairs 4. A comple... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-2. (Adjective.) Related to the complex numbers.
3. The (line) complex group is an old name for the symplectic group.
composite Reducible (meaning having more than one irreducible component).
conchoid A conchoid is the curve given by the cissoid of a circle and another curve. S... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-concomitant A (mixed) concomitant is an invariant homogeneous polynomial in the coefficients of a form, a covariant variable, and a contravariant variable. In other words it is a (tri)homogeneous polynomial on SV⊕V⊕V* for some vector space V, where SV is some symmetric power o... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-configuration A configuration is a finite set of points and lines (and sometimes planes), generally with equal numbers of points per line and equal numbers of lines per point.
confocal Having the same foci congruence A family of lines in projective space such that there are a ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-contravariant 1. A bihomogeneous polynomial in dual variables of x, y, ... and the coefficients of some homogeneous form in x, y,... that is invariant under some group of linear transformations. In other words it is a bihomogeneous polynomial on SV⊕V for some vector space V, w... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-coplanar In the same plane correlation An isomorphism from a projective space to the dual of a projective space, often to the dual of itself. A correlation on the projective space of a vector space is essentially the same as a nonsingular bilinear form on the vector space, up ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-C-crunode Crunode is an archaic term for a node, a double point with distinct tangent directions.
cubic Degree 3, especially a degree 3 projective variety cubo-cubic A cubo-cubic transformation is a Cremona transformation such that the homaloids of the transformation and its inv... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-decic decimic 1. (Adjective) Degree 10 2. (Noun) A degree 10 projective variety deficiency 1. The deficiency of a linear system is its codimension in the corresponding complete linear system. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-2. The deficiency D of a plane curve is an approximation to its genus, equal to the genus when all singular points are ordinary, given by (n–1)(n–2)/2 –(a–1)(a–2)/2 – (b–1)(b–2)/2 –..., where n is the degree of the curve and a. b, ... are the multiplicities of its singular poi... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-desmic system A desmic system is a configuration of three desmic tetrahedra.
developable 1. (Noun) A 1-dimensional family of planes in 3-dimensional projective space (Semple & Roth 1949, p.85).
2. (Noun) The envelope of the normals of a curve 3. (Noun) Short for a developable ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-2. A differential of the second kind is a meromorphic 1-form such that the residues of all poles are 0. Sometimes it is only allowd to have one pole that must be of order 2. 3. A differential of the third kind is sometimes a meromorphic 1-form such that all poles are simple (... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-director The director circle of a conic is the locus of points where two orthogonal tangent lines to the conic meet. More generally the director conic of a conic in regard to two points is defined in a similar way. (Baker 1922b, vol 2, p. 26) directrix A straight line, or mor... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-D-double curve A 1-dimensional singularity, usually of a surface, of multiplicity 2 double point 1. A 0-dimensional singularity of multiplicity 2, such as a node.
One of the two points fixed by an involution of a projective line. (Baker 1922b, vol 2, p.3) double six The Schläfl... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-E-env Eckardt point An Eckardt point is a point of intersection of 3 lines on a cubic surface.
effective An effective cycle or divisor is one with no negative coefficients elation A collineation that fixes all points on a line (called its axis) and all lines though a point on th... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-E-exceptional 1. Corresponding to something of lower dimension under a birational correspondence, as in exceptional curve, exceptional divisor 2. An exceptional curve on a surface is one that corresponds to a simple point on another surface under a birational correspondence. It ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-F-facultative A facultative point is one where a given function is positive. (Salmon 1885, p.243) first kind holomorphic or regular (when applied to differentials) flat 1. (Noun) A linear subspace of projective space, such as a point, line, plane, hyperplane.
2. (Adjective) Hav... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-F-flex Short for point of inflection focal 1. A focal point, line, plane, ... is the intersection of several consecutive elements of a family of linear subspaces. (Semple & Roth 1949, p. 85, 252) 2. A focal curve, surface and so on is the locus of the focal points of a family of... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-F-2. A differential form.
free intersection An intersection point of two members of a family that is not a base point.
freedom Dimension, as in degrees of freedom. (Semple & Roth 1949, p.26).
fundamental This term seem to be ambiguous and poorly defined: Zariski states: "I can f... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-G-grd, γrd A linear or algebraic system of divisors of dimension r and degree d on a curve. The letter g is used for linear systems, and the letter γ is used for algebraic systems.
generator One of the lines of a ruled surface (Semple & Roth 1949, p.204) or more generally an ele... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-G-grade The grade of a linear system of divisors on an n-dimensional variety is the number of free intersection points of n generic divisors. In particular the grade of a linear series of divisors on a curve is now called the degree and is the number of points in each divisor (S... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-harmonic 1. Two pairs of points on a line are harmonic if their cross ratio is –1. The 4 points are called a harmonic set, and the points of one pair are called harmonic conjugates with respect to the other pair. 2. A harmonic cubic is an elliptic curve with j-invariant 1728,... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-3. Satisfying some analogue of the Laplace equation, as in harmonic form. | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-4. The harmonic polar line of an inflection point of a cubic curve is the component of the polar conic other than the tangent line. (Dolgachev 2012, 3.1.2) 5. A harmonic net is a set of points on a line containing the harmonic conjugate of any point with respect to any other ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-1. A Hessian matrix, or a variety associated with it. See Salmon (1879, p.55). | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-2. The Hessian line is a line associated to 3 points A, B, C, of a conic, containing the three points given by the intersections of the tangents at A, B, C with the lines BC, CA, AB. 3. The Hessian point is a point associated to three lines tangent to a conic, whose construct... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-4. The Hessian pair or Hessian duad of three points on a projective line is the pair of points fixed by the projective transformations of order 3 permuting the 3 points. More generally the Hessian pair is also defined in a similar way for triples of points of a rational curve,... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-H-6. The Hesse group is the group of automorphisms of the Hesse configuration, of order 216.
hexad A set of 6 points homaloid An element of a homaloidal system, in particular the image of a hyperlpane under a Cremona transformation.
homaloidal 1. A homaloidal linear system of di... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-I-index of speciality The dimension of the first cohomology group of the line bundle of a divisor D; often denoted by i or i(D). Semple & Roth (1949, p.381) infinitely near point A point on a blow up of a variety inflection inflexion An inflection is a point where the curvatur... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-I-2. Tangent to some lines, as in inscribed circle.
integral An integral is (more or less) what is now called a closed differential form, or sometimes the result of integrating such a form.. 1. An integral of the first kind is a holomorphic closed differential form.
2. An integ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-J-Jacobian 1. The Jacobian variety of a curve 2. A Jacobian curve; see below Jacobian curve The locus of double points of curves of a net. (Semple & Roth 1949, p.115) Jacobian set The set of free double points of a pencil of curves. (Semple & Roth 1949, p.119) Jacobian system Th... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-K-kenotheme An intersection of n hypersurfaces in n-dimensional projective space. (Sylvester 1853, Glossary p. 543–548) Archaic. keratoid Horn-like. A keratoid cusp is one whose two branches curve in opposite direction; see ramphoid cusp. Salmon (1879) Kirkman point One of the ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-L-Laguerre net A net V of plane curves of some degree d such that the base locus of a generic pencil of V is the base locus of V together with d–1 collinear points (Dolgachev 2012, theorem 7.3.5) (Coolidge 1931, p. 423) lemniscate A lemniscate is a curve resembling a figure 8. S... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-L-line coordinates Projective coordinates. See Salmon (1879, p. 7) linear Degree 1 linear system A linear system of divisors, given by the zeros of elements of a vector space of sections of a line bundle locus 1-A subset of projective space given by points satisfying some condit... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-M-manifold An algebraic manifold is a cycle of projective space, in other words a formal linear combination of irreducible subvarieties. Algebraic manifolds may have singularities, so their underlying topological spaces need not be manifolds in the sense of differential topology... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-M-Möbius tetrads Two tetrads such that the plane containing any three points of one tetrad contains a point of the other. (Baker 1922a, vol 1, p. 62) model 1. A variety whose points (or sometimes hyperplane sections) correspond to elements of some family. Similar to what is now... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-M-modulus A function of algebraic varieties depending only on the isomorphism type; in other words, a function on a moduli space Moebius tetrads See #Möbius tetrads monoid A surface of degree n with a point of multiplicity n–1. (Semple & Roth 1949, p.187) monoidal transformatio... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-M-multiplicity The multiplicity of a point on a hypersurface is the degree of the first non-vanishing coefficient of the Taylor series at the point. More generally one can define the multiplicity of any point of a variety as the multiplicity of its local ring. A point has multip... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-N-Néron–Severi group The Néron–Severi group is the group of divisors module numerical equivalence.
nest Two components (circuits) of a real algebraic curve are said to nest if one is inside the other. (Coolidge 1931) net 1. A 2-dimensional linear system. See "pencil" and "web". ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-N-nodal A nodal tangent to a singular point of a curve is one of the lines of its tangent cone. (Semple & Roth 1949, p.26) node A singular point p of a hypersurface f = 0, usually with the determinant of the Hessian of f not zero at p. (Cayley 1852) node cusp A singularity of a ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-N-2. Orthogonal to the tangent space, such as a line orthogonal to the tangent space or the normal bundle.
3. A normal intersection is an intersection with the "expected" codimension (given a sum of codimensions). (Semple & Roth 1949, p.16) 4. Local rings are integrally closed; ... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-O-octad A set of 8 points octic 1. (Adjective) Degree 8 2. (Noun) A degree 8 projective variety ombilic The curve at infinity which is the intersection of any sphere with the plane at infinity. All points of the ombilic are non-real.
order 1. Now called degree of an algebraic va... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-Pappus 1. Pappus of Alexandria.
2. The Pappus configuration is the configuration of 9 lines and 9 points that occurs in Pappus's hexagon theorem.
parabolic point A point of a variety that also lies in the Hessian.
parallel 1. Meeting at the line or plane at infinity, as in par... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-Pascal Short for Pascal line, the line determined by 6 points of a conic in Pascal's theorem pedal The pedal curve of C with respect to a pedal point P is the locus of points X such that the line through X orthogonal to PX is tangent to C. (Salmon 1879, p.96) pencil A 1-dimens... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-pentad A set of 5 points pentahedron A union of 5 planes, in particular the Sylvester pentahedron of a cubic surface.
period The integral of a differential form over a submanifold perspectivity An isomorphism between two projective lines (or ranges) of projective space such th... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-perspector The center of a perspectivity perspectrix The line in Desargues theorem on which the intersections of pairs of sides of two perspective triangles lie pinch A pinch point is a singular point of a surface, where the two tangent planes of a point on a double curve coin... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-Plücker 1. For Plücker characteristic see characteristic 2. A Plücker line is one of the 15 lines containing 4 of the 20 Steiner points associated to 6 points on a conic. The Plücker lines meet in threes at the 60 Kirkman points. (Dolgachev 2012, p.124) plurigenus Plural plu... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-point-star A family of lines with a common point polar 1. (Adjective) Related by a polarity 2. The polar conic is the zero set of the quadratic form associated to a polarity, or equivalently the set of self-conjugate points of the polarity.
3. (Noun) The first polar, second po... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-poloconic polocubic poloquartic The poloconic (also called conic polar) of a line in the plane with respect to a cubic curve is the locus of points whose first polar is tangent to the line. (Dolgachev 2012, p. 156–157) polygonal A polygonal (or k-gonal) curve is a curve toget... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-porism 1. A porism is a corollary, especially in geometry, as in Poncelet's porism. The precise meaning seems to be controversial.
2. An arrangement of geometrical figures (such as lines or circles) that are inscribed in one curve and circumscribed around another, as in Poncel... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-poristic Having either no solutions or infinitely many (Semple & Roth 1949, p.186). For example, Poncelet's porism and Steiner's porism imply that if there is one way to arrange lines or circles then there are infinitely many ways. postulated A postulated object (point, line,... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-P-propinquity A number depending on two branches at a point, defined by Coolidge (1931, p. 224).
proximate For proximate points see (Zariski 1935, p.9). pure All components are of the same dimension. Now called equidimensional. (Semple & Roth 1949, p.15) | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Q-quadratic transformation 1. A Cremona transformation of degree 2. A standard quadratic transformation is one similar to the map taking each coordinate to its inverse.
2. A monomial transformation with center a point, or in other words a blowup at a point.
quadric Degree 2, esp... | milkshake721/2.1M-wiki-STEM |
Glossary of classical algebraic geometry-Q-quadrisecant A quadrisecant is a line meeting something in four points quadro-cubic, quadro-quartic A quadro-cubic or quadro-quartic transformation is a Cremona transformation such that the homaloids of the transformation have degree 2 and those of its inverse have degree 3 or... | milkshake721/2.1M-wiki-STEM |
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