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- ...[[polynomial]]s. It is also called a '''regular map'''. A morphism from an algebraic variety to the [[affine line]] is also called a '''regular function'''. ...e are no non-constant regular functions on [[projective variety|projective varieties]] – the concepts of [[rational map|rational]] and [[birational]] maps are w ...26 KB (4,269 words) - 16:03, 8 February 2025
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- ...humb|right|The [[Riemann sphere]] is one of the simplest complex algebraic varieties.]] ...Shafarevich]], eds. ''Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians.'' Vol. 3. Springer, 1998. {{ISBN|3-540-54681-2} ...2 KB (282 words) - 17:23, 7 February 2024
- ...r (''X'', ''D'') consisting of a [[normal variety]] ''X'' and a [[divisor (algebraic geometry)#Q-divisors|<math>\mathbb{Q}</math>-divisor]] ''D'' on ''X'' (e.g. ...s | last2=Mori | first2=Shigefumi | title=Birational geometry of algebraic varieties | publisher=[[Cambridge University Press]] | series=Cambridge Tracts in Mat ...749 bytes (93 words) - 08:24, 13 May 2024
- ...tics, the '''Suslin homology''' is a homology theory attached to algebraic varieties. It was proposed by Suslin in 1987, and developed by {{harvs|txt|last1=Susl *{{citation|mr=1432056 |last=Levine|first= Marc|title=Homology of algebraic varieties: an introduction to the works of Suslin and Voevodsky|journal=Bull. Amer. M ...1 KB (214 words) - 02:19, 15 April 2020
- ...o <math>\mathbb{R}^{2n}</math> for some ''n'', but is not isomorphic as an algebraic variety to <math>\mathbb{C}^n</math>.<ref>{{citation ...e role of exotic affine spaces in the classification of homogeneous affine varieties ...3 KB (325 words) - 22:06, 15 August 2023
- == Finite morphisms in algebraic geometry == ...the simplest case of [[affine variety|affine varieties]], given two affine varieties <math>V\subseteq\mathbb{A}^n</math>, <math>W\subseteq\mathbb{A}^m</math> an ...2 KB (348 words) - 18:23, 6 February 2024
- {{short description|Constructs the minimal model of a given smooth algebraic surface}} ...to construct the [[minimal model program|minimal model]] of a given smooth algebraic surface. ...2 KB (281 words) - 01:47, 22 October 2024
- ...ion ''h'' and a linear transformation ''X''. The study of Hessenberg varieties was first motivated by questions in [[numerical analysis]] in relation to a Some examples of Hessenberg varieties (with their <math>h</math> function) include: ...2 KB (329 words) - 10:46, 9 October 2024
- In algebraic geometry, the '''quotient space''' of an [[algebraic stack]] ''F'', denoted by |''F''|, is a [[topological space]] which as a se ...o |X|</math> is functorial; i.e., each morphism <math>f: X \to Y</math> of algebraic stacks determines a continuous map <math>f: |X| \to |Y|</math>. ...2 KB (248 words) - 03:12, 4 December 2019
- ...'''algebraic fiber space''', as it is an analog of a [[fiber space]] in [[algebraic topology]]. ...s | last2=Mori | first2=Shigefumi | title=Birational geometry of algebraic varieties | publisher=[[Cambridge University Press]] | series=Cambridge Tracts in Mat ...2 KB (307 words) - 09:52, 29 November 2024
- {{Short description|Analogue of homotopy type for algebraic varieties}} ...omotopy type]] of [[topological space]]s for [[algebraic variety|algebraic varieties]]. ...2 KB (283 words) - 07:01, 21 December 2021
- ...|series=Second Series | year=1989 | title=Multiplicity estimates on group varieties | volume=129 | number=3 | pages=471–500 | doi=10.2307/1971514 | jstor=19715 ...less <math>A</math> contains a proper [[Algebraic group#Algebraic subgroup|algebraic subgroup]]. ...4 KB (485 words) - 01:39, 16 November 2022
- In [[algebraic geometry]], given a [[category (mathematics)|category]] ''C'', a '''categor ...y]] was the construction of a categorical quotient for [[algebraic variety|varieties]] or [[scheme (mathematics)|scheme]]s. ...2 KB (274 words) - 21:45, 12 August 2023
- {{Short description|Concept in algebraic geometry}} ...e existence of [[semistable reduction|semistable reductions]] of algebraic varieties over one-dimensional bases. ...2 KB (287 words) - 15:33, 30 March 2024
- ...ath>.<ref name=":0">{{Cite web|last=Arapura|first=Donu|date=|title=Abelian Varieties and Moduli|url=https://www.math.purdue.edu/~arapura/preprints/abelian.pdf|a === Principally polarized Abelian varieties === ...5 KB (824 words) - 17:32, 19 February 2025
- ...ieties]], then a polynomial mapping is precisely a [[morphism of algebraic varieties]]. ...1 KB (229 words) - 06:23, 13 May 2024
- In [[algebraic geometry]] a '''normal crossing singularity''' is a singularity similar to ...raic geometry]], '''normal crossing divisors''' are a class of [[Divisor (algebraic geometry)|divisors]] which generalize the smooth divisors. Intuitively they ...3 KB (381 words) - 16:57, 18 February 2017
- ...ndation for the definition of [[invertible sheaf|invertible sheaves]] in [[algebraic geometry]]. ...n]] one [[algebraic variety|varieties]] including the theory of [[divisor (algebraic geometry)|divisor]]s. ...1 KB (184 words) - 04:53, 4 May 2024
- {{Short description|Mathematical theory in the field of algebraic geometry}} In algebraic geometry, '''semistable reduction theorems''' state that, given a proper fl ...4 KB (614 words) - 16:51, 16 February 2024
- ...=en-US|access-date=2019-08-05}}</ref> American mathematician, working in [[algebraic geometry]]. ...ry (such as [[Gröbner basis]]), [[Torelli set]]s and [[toric variety|toric varieties]], and [[history of mathematics]]. He is also known for several textbooks. ...4 KB (539 words) - 23:10, 5 February 2024
- {{Short description|On heights of points on algebraic varieties over number fields}} ...a|authorlink=Paul Vojta|year=1987}} about heights of points on [[algebraic varieties]] over [[number field]]s. The conjecture was motivated by an analogy betwee ...4 KB (604 words) - 06:27, 13 December 2024