Serre duality
In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexander Grothendieck found wide generalizations, for example to singular varieties. On an n-dimensional variety, the theorem says that a cohomology group is the dual space of another one, . Serre duality is the analog for coherent sheaf cohomology of Poincaré duality in topology, with the canonical line bundle replacing the orientation sheaf.
Wikipage redirect
Adele ringAdjoint functorsBrill–Noether theoryCanonical bundleCohen–Macaulay ringCoherent dualityCoherent sheafDeformation (mathematics)Derived categoryDolbeault cohomologyDuality (mathematics)Dualizing sheafEnriques–Kodaira classificationGeometric genusGlossary of algebraic geometryGorenstein ringGorenstein schemeGrothendieck local dualityHasse–Witt matrixHirzebruch–Riemann–Roch theoremHitchin systemHodge theoryHolomorphic vector bundleK3 surfaceKodaira vanishing theoremKähler differentialKähler manifoldList of algebraic geometry topicsList of dualitiesList of things named after Jean-Pierre SerreLocal cohomologyMirror symmetry conjectureModuli of algebraic curvesNonabelian Hodge correspondenceNoncommutative geometryProjective varietyRiemann–Roch theoremRiemann–Roch theorem for surfacesScientific phenomena named after peopleSerre's duality theorem
Link from a Wikipage to another Wikipage
primaryTopic
Serre duality
In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre. The basic version applies to vector bundles on a smooth projective variety, but Alexander Grothendieck found wide generalizations, for example to singular varieties. On an n-dimensional variety, the theorem says that a cohomology group is the dual space of another one, . Serre duality is the analog for coherent sheaf cohomology of Poincaré duality in topology, with the canonical line bundle replacing the orientation sheaf.
has abstract
In algebraic geometry, a branc ...... ology to Dolbeault cohomology.
@en
Link from a Wikipage to an external page
Wikipage page ID
page length (characters) of wiki page
Wikipage revision ID
1,021,828,398
Link from a Wikipage to another Wikipage
id
D/d034120
@en
title
Duality
@en
wikiPageUsesTemplate
comment
In algebraic geometry, a branc ...... placing the orientation sheaf.
@en
label
Serre duality
@en