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0answers
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Cohomology of Sym(E) [closed]

Let $U,V$ be two vector bundles on some scheme $X$. Let $E$ be some bundle in $0\to U\to E\to V\to 0$. If I can show that $H^i(X; Sym(U\oplus V))=0$ for $i>0$, can we conclude the same property for ...
7
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1answer
253 views

Vanishing theorems in positive characteristic

In the paper Deligne, Pierre; Illusie, Luc (1987), "Relèvements modulo $p^{2}$ et décomposition du complexe de De Rham", Inventiones Mathematicae 89 (2): 247–270, doi:10.1007/BF01389078 I found the ...
4
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2answers
403 views

English reference for the Grauert–Riemenschneider vanishing theorem

What is the best reference in English for the following theorem of Grauert–Riemenschneider: Theorem: Let $\phi:X \to Y$ be a proper bi-rational morphism of algebraic varieties over characteristic ...
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0answers
130 views

vanishing theorem for Nakano k-positive vector bundles ?

Hi, The Nakano vanishing theorem for vector bundles says apparently the following: Let $X$ be a compact kähler manifold of dimension $n$, and $E$ an hermitian holomorphic vector bundle. If $E$ if ...