Serre duality is a fundamental theorem in algebraic geometry that establishes a relationship between the cohomology groups of a projective variety and its dual. It asserts that for a smooth projective variety, the higher cohomology groups of certain sheaves are isomorphic to the cohomology groups of the dual sheaf, revealing deep connections between geometry and algebraic topology. This concept is crucial in understanding how geometric properties translate into algebraic structures, especially in the context of Kähler manifolds and Hodge theory.
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