In mathematics, the Grauert–Riemenschneider vanishing theorem is an extension of the Kodaira vanishing theorem on the vanishing of higher cohomology groups of coherent sheaves on a compact complex manifold, due to .
Grauert–Riemenschneider conjecture The Grauert–Riemenschneider conjecture is a conjecture related to the Grauert–Riemenschneider vanishing theorem:
This conjecture was proved by using the Riemann–Roch type theorem (Hirzebruch–Riemann–Roch theorem) and by using Morse theory.
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