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serred
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In algebraic geometry, a branch of mathematics, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves). It shows that a cohomology group Hi is the dual space of another one, Hn−i. * In the case for holomorphic vector bundle E over a smooth compact complex manifold V, the statement is in the form:* * * * * H * * q * * * ( * V * , * E * ) * ≅ * * H * * n * − * q * * * ( * V * , * K * ⊗ * * E * * ∗ * * * * ) * * ∗ * * * , * * * {\displaystyle H^{q}(V,E)\cong H^{n-q}(V,K\otimes E^{\ast })^{\ast },} * in which V is not necessarily projective. |