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What (who) is vanishing theorem - definition
Vanishing theorem
WIKIMEDIA DISAMBIGUATION PAGE
Vanishing theorem (disambiguation)
In algebraic geometry, a vanishing theorem gives conditions for coherent cohomology groups to vanish.
Nakano vanishing theorem
GENERALIZES THE KODAIRA VANISHING THEOREM
Akizuki–Nakano vanishing theorem; Draft:Nakano's vanishing theorem; Nakano's vanishing theorem; Kodaira–Nakano vanishing theorem
In mathematics, specifically in the study of vector bundles over complex Kähler manifolds, the Nakano vanishing theorem, sometimes called the Akizuki–Nakano vanishing theorem, generalizes the Kodaira vanishing theorem. Given a compact complex manifold M with a holomorphic line bundle F over M, the Nakano vanishing theorem provides a condition on when the cohomology groups H^q(M; \Omega^p(F)) equal zero.
Kodaira vanishing theorem
THEOREM GIVING GENERAL CONDITIONS UNDER WHICH POSITIVE-DEGREE SHEAF COHOMOLOGY GROUPS VANISH
Kodaira-Nakano vanishing theorem; Kodaira vanishing theory; Akizuki-Nakano vanishing theorem; Kodaira's vanishing theorem
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.
