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#kodaira_vanishing_theorem

Kodaira vanishing theorem

Gives general conditions under which sheaf cohomology groups with indices > 0 are zero

In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero. The implications for the group with index q = 0 is usually that its dimension — the number of independent global sections — coincides with a holomorphic Euler characteristic that can be computed using the Hirzebruch–Riemann–Roch theorem.

Fri 26th

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