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- {{short description|Number of points needed to determine an algebraic curve}} ...number of points in the real [[plane (mathematics)|plane]] falling on an [[algebraic curve]] to uniquely determine the curve in non-[[Degeneracy (mathematics)|d ...6 KB (1,017 words) - 09:34, 12 May 2024
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- ...and {{pi}} has degree ''d''.<ref>Joe Harris and Ian Morrison. ''Moduli of curves.'' {{algebraic-geometry-stub}} ...385 bytes (56 words) - 06:58, 29 June 2019
- ...''<sup>''n''</sup> of maximal genus ''g'' among irreducible non-degenerate curves of given degree ''d''. Castelnuovo described the curves satisfying this bound, showing in particular that they lie on either a rati ...1 KB (166 words) - 15:19, 14 October 2015
- ...r1=Friedlander, Eric |editor2=Grayson, Daniel |chapter=Algebraic K-Theory, Algebraic Cycles and Arithmetic Geometry}}</ref> ==Curves== ...2 KB (287 words) - 05:50, 22 June 2022
- ...ions to the theory of [[modular form]]s on [[reductive group|reductive]] [[algebraic groups]]<ref>{{Citation ...{C}_g\rightarrow\mathcal{M}_g</math> be the [[universal object|universal]] algebraic curve of genus ''g'' and let <math>\omega_g</math> be its [[relative dualiz ...3 KB (363 words) - 15:59, 30 June 2019
- [[File:Steinmetz-kurve.svg|300px|thumb|Steinmetz curves for various cases]] ...|thumb|Steinmetz solid (intersection of two cylinders) involving Steinmetz curves (purple)]] ...2 KB (262 words) - 17:20, 1 June 2024
- ...orphisms, necessitating the construction of the [[Moduli stack of elliptic curves]]. | title = Arithmetic moduli of elliptic curves ...2 KB (343 words) - 12:52, 8 November 2024
- {{Short description|Algebraic concept}} ...valuation ring]].<ref>J. H. Silverman (1986). ''The arithmetic of elliptic curves''. Springer. p. 21</ref> This valuation will show a way to count the order ...3 KB (596 words) - 01:40, 7 January 2023
- ...ge's conjecture''' is a theorem about stability of [[vector bundle]]s over curves, introduced by {{ill|Herbert_Lange_(mathematician)|lt=Herbet Lange|de|Herbe ...be a smooth projective [[algebraic curve|curve]] of [[Genus (mathematics)#Algebraic geometry|genus]] greater or equal to 2. For [[generic property|generic]] ve ...3 KB (403 words) - 00:16, 10 November 2024
- ...ugel.svg|thumb|right|The [[Riemann sphere]] is one of the simplest complex algebraic varieties.]] ...h]], eds. ''Algebraic Geometry III: Complex Algebraic Varieties. Algebraic Curves and Their Jacobians.'' Vol. 3. Springer, 1998. {{ISBN|3-540-54681-2}}</ref> ...2 KB (282 words) - 17:23, 7 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
- {{Short description|Theorem in classical algebraic geometry}} In classical [[algebraic geometry]], the '''genus–degree formula''' relates the degree <math>d</math ...4 KB (612 words) - 11:27, 10 December 2024
- {{short description|Object in algebraic geometry}} ...tacky curve''' is an object in [[algebraic geometry]] that is roughly an [[algebraic curve]] with potentially "fractional points" called '''stacky points'''. A ...5 KB (631 words) - 04:00, 1 March 2024
- {{short description|1=Family of curves of the form r^n = a^n cos(nθ)}} In [[algebraic geometry]], the '''sinusoidal spirals''' are a family of curves defined by the equation in [[polar coordinates]] ...4 KB (587 words) - 06:52, 6 April 2024
- ...a special [[quintic threefold]], in other words a [[Glossary of classical algebraic geometry#D|degree]] 5, [[dimension]] 3 [[hypersurface]] in 4-dimensional co ==Rational curves== ...3 KB (335 words) - 20:07, 28 April 2021
- ...families of [[Stable vector bundle|semistable]] [[vector bundle]]s on an [[algebraic curve]]. [[Category:Algebraic curves]] ...1 KB (158 words) - 22:01, 5 June 2023
- ...'''algebraic fiber space''', as it is an analog of a [[fiber space]] in [[algebraic topology]]. ...y and <math>\overline{NS}(X)</math> the closure of the span of irreducible curves on <math>X</math> in <math>N_1(X)</math> = the real vector space of numeric ...2 KB (307 words) - 09:52, 29 November 2024
- ...erential form on a [[smooth morphism|smooth]] [[proper morphism|proper]] [[algebraic curve]] vanishes. ...[[field (mathematics)|field]] ''k''. A meromorphic [[Kähler differential|(algebraic) differential form]] <math>\omega</math> has, at each [[closed point]] ''x' ...2 KB (353 words) - 02:56, 19 February 2025
- ...nn F.|date=1983-12-01|title=The projectivity of the moduli space of stable curves, II: The stacks $M_{g,n}$|url=https://www.mscand.dk/article/view/12001|jour ...)</math></blockquote>An element of <math>x \in F(X)</math> is called an '''algebraic element''' if it is the henselization of an <math>\mathcal{O}_S</math>-alge ...4 KB (606 words) - 21:47, 12 August 2023
- ...s sextic''' is a degree 6 [[plane curve]] with four [[Singular point of an algebraic variety|nodes]] studied by {{harvs|txt|last=Wiman|first=Anders|authorlink=A ...[[Normalization of an algebraic variety|normalization]] is a [[genus of an algebraic curve|genus]] 6 curve with [[automorphism group]] isomorphic to the [[symme ...1 KB (160 words) - 15:42, 28 October 2022
- {{Short description|Type of object in algebraic geometry}} In [[algebraic geometry]], a '''Deligne–Mumford stack''' is a [[stack (mathematics)|stack] ...4 KB (616 words) - 11:21, 18 May 2024