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...stanford.edu/~vakil/0708-216/216class38.pdf|title=Foundations of algebraic geometry class 38|first=Ravi|last=Vakil|publisher=Stanford University|year=2007–2008 There is yet another projection formula in the setting of [[étale cohomology]]. ...

{{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. ...

...r=2373099| url=http://nrs.harvard.edu/urn-3:HUL.InstRepos:3597248 }}</ref> in 1967 states that if ''L'' is a semi-ample [[invertible sheaf]] with [[Iitak [[Category:Theorems in algebraic geometry]] ...

{{short description|Result in algebraic K-theory relating Chow groups to cohomology}} ...matics)|field]] is isomorphic to the cohomology of ''X'' with coefficients in the K-theory of the structure sheaf <math>\mathcal{O}_X</math>; that is, ...

...algebraic subsets of ''X'' there is a fundamental system of neighborhoods (in the classical topology) of ''x'' whose intersection with ''Y'' is connected ...and geometrically unibranch points are used in some theorems in algebraic geometry. For example, there is the following result: ...

{{Short description|Criterion for vector stability in algebraic geometry}} ...ion for the [[Geometric invariant theory#Stability|stability]] of a vector in a [[group representation|representation]] of a complex [[reductive group]]. ...

...book|url=https://books.google.com/books?id=ePf_AwAAQBAJ|title=Differential Geometry of Complex Vector Bundles|last=Kobayashi|first=Shoshichi|date=2014-07-14|pu ...first2=Shigeo|date=1954|title=Note on Kodaira-Spencer's proof of Lefschetz theorems|url=https://projecteuclid.org/euclid.pja/1195526105|journal=Proceedings of ...

In [[algebraic geometry]], '''Reider's theorem''' gives conditions for a [[line bundle]] on a proje Let ''D'' be a [[Nef line bundle|nef]] [[divisor (algebraic geometry)|divisor]] on a smooth projective surface ''X''. Denote by ''K''<sub>''X''< ...

{{Short description|Algebraic geometry theorem}} ...7}}, is a condition on the second-order elements of the points of a plane algebraic curve meeting a given line. ...

...n invariant neighborhood of <math>G/G_x</math> (viewed as a zero section) in <math>G \times_{G_x} T_x M / T_x(G \cdot x)</math> so that it defines an [[ In [[algebraic geometry]], there is an analog of the slice theorem; it is called [[Luna's slice the ...

In [[real algebraic geometry]], '''Gudkov's conjecture''', also called '''Gudkov’s congruence''', (named ...t=Vladimir I.|last=Arnold|authorlink=Vladimir Arnold| title=Real Algebraic Geometry|url=https://books.google.com/books?id=xchAAAAAQBAJ&pg=PA95|year=2013|publis ...

In [[mathematics]], the '''Holomorphic Lefschetz formula''' is an analogue for ...| author2-link=Joe Harris (mathematician) | title=Principles of algebraic geometry | publisher=[[John Wiley & Sons]] | location=New York | series=Wiley Classi ...

...</ref> and proved by [[Montserrat Teixidor i Bigas]] and [[Barbara Russo]] in 1999. ...th projective [[algebraic curve|curve]] of [[Genus (mathematics)#Algebraic geometry|genus]] greater or equal to 2. For [[generic property|generic]] vector bund ...

{{Short description|Theorem in complex analysis about the sheaf of holomorphic functions}} ...h>) is [[coherent sheaf|coherent]].<ref>{{harvtxt|Noguchi|2019}}</ref><ref>In {{harvtxt|Oka|1950}} paper it was called the [[idéal de domaines indétermin ...

{{Short description|Theorem in geometry}} In algebraic geometry, there are various generalizations of the [[Riemann–Roch theorem]]; among t ...

...id are the purely algebraic analogue of this construction, giving a purely algebraic description of quasi-coherent sheaves on a stack: this is one of the first == Structure theorems == ...

...braic scheme ''X'' with [[linear algebraic group action|action of a linear algebraic group]] ''G'', via Quillen's [[Q-construction]]; thus, by definition, ...2–1995)].</ref> Specifically, he proved equivariant analogs of fundamental theorems such as the localization theorem. ...

...af]] of [[ideal (ring theory)|ideals]] over a [[complex number|complex]] [[algebraic variety|variety]] and a real number ''c'' consists (locally) of the functio Multiplier ideals are discussed in the survey articles {{harvtxt|Blickle|Lazarsfeld|2004}}, {{harvtxt|Siu|2005 ...

In [[algebraic geometry]], the '''Atiyah–Bott formula''' says<ref>{{harvnb|Gaitsgory|Lurie|2019|loc [[Category:Theorems in algebraic geometry]] ...

...f a torus ''T'' is called a '''<nowiki />''T''-variety'''. In differential geometry, one considers an action of a real or complex torus on a manifold (or an [[ A [[normal scheme|normal]] algebraic variety with a torus acting on it in such a way that there is a dense orbit is called a [[toric variety]] (for e ...