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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…

Products, Serre duality for vector bundles & Serre duality for coherent sheaves

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Overview

Serre duality for vector bundles

Algebraic curves

Serre duality for coherent sheaves

Grothendieck duality

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Map overview Semantic statistics

Serre duality

Nodes75
Edges74
Triples52
Avg. degree1.97
Density0.026667
Components1

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Serre duality

Top relations

related to Complex moduli of Calabi–Yau threefolds · 12
Serre duality → Bogomolev, Calabi, Hodge, In, Of, Omega, Serre, Since, Tian, Todorov, TX, Yau
related to Grothendieck duality · 11
Serre duality → Cohen, For, Formally, Grothendieck's, In, Macaulay, Namely, Serre, Spec, Using, When
related to Serre duality for coherent sheaves · 10
Serre duality → Another, As, Cohen, For, Grothendieck, Macaulay, Namely, Serre, Some, Suppose
related to Differential-geometric theorem · 7
Serre duality → Additionally, Here, Hodge, Namely, Riemannian, Serre, The Hodge
related to Algebraic curves · 6
Serre duality → For, Over, Riemann, Roch, Serre, That
related to Algebraic theorem · 4
Serre duality → Define, Let, Suppose, Then Serre
is a · 2
Serre duality → analog for coherent sheaf cohomology of Poincaré duality in topology, duality for the coherent sheaf cohomology of algebraic varieties

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Important terminology

displaystyle duality serre complex bundle sheaf theorem cohomology algebraic omega line vector projective coherent smooth isomorphism degree dualizing space canonical

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Serre dualityis aduality for the coherent sheaf cohomology of algebraic varieties0.90text
Serre dualityis aanalog for coherent sheaf cohomology of Poincaré duality in topology0.90text
Serre dualityrelated to Algebraic curvesSerre0.60section
Serre dualityrelated to Algebraic curvesOver0.60section
Serre dualityrelated to Algebraic curvesRiemann0.60section
Serre dualityrelated to Algebraic curvesFor0.60section
Serre dualityrelated to Algebraic curvesThat0.60section
Serre dualityrelated to Algebraic curvesRoch0.60section
Serre dualityrelated to Algebraic theoremLet0.60section
Serre dualityrelated to Algebraic theoremDefine0.60section
Serre dualityrelated to Algebraic theoremSuppose0.60section
Serre dualityrelated to Algebraic theoremThen Serre0.60section

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