Grauert–Riemenschneider vanishing theorem explained
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.
References
- 10.5802/aif.1034. Champs magnétiques et inégalités de Morse pour la $d$-cohomologie . 1985 . Demailly . Jean-Pierre . Annales de l'Institut Fourier . 35 . 4 . 189–229 . free .
- 10.4310/JDG/1214438686. A vanishing theorem for semipositive line bundles over non-Kähler manifolds . 1984 . Siu . Yam Tong . Journal of Differential Geometry . 19 . 2 . free .
- Book: 10.1007/BFB0084590. Some recent results in complex manifold theory related to vanishing theorems for the semipositive case . Arbeitstagung Bonn 1984 . Lecture Notes in Mathematics . 1985 . Siu . Yum-Tong . 1111 . 169–192 . 978-3-540-15195-1 .
