Questions tagged [vanishing]
The vanishing tag has no usage guidance.
8
questions
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Vanishing of a Higher Brauer group of a field
Let $k$ be a field. I am interested in the notion of the higher Brauer group defined as follows: For X a smooth scheme over $k$, $Br^r(X):=H^{2r+1}_{et}(X, \mathbb{Z}(r))$, an etale motivic cohomology ...
- 431
3
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0
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Sheaf cohomology of the complement of a schubert variety
Let $k$ be a field, $d,n \in \mathbb{N}$ and denote by $Gr(d,n)$ the Grassmannian, which parameterizes the $d$-dimensional linear subspaces of $n$-dimensional $k$-vector space, considered as a ...
- 473
9
votes
2
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Nakano vanishing in positive characteristic
Let $X$ be a smooth projective variety defined over a field $k$.
In characteristic zero, the following is a special case of the (Kodaira-Akizuki-)Nakano vanishing theorem:
$(\ast) \quad$ $\mathrm H^...
- 1,072
5
votes
2
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661
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Log canonical counterexample to Kawamata-Viehweg vanishing
I found in the literature that, in characteristic 0, Kodaira vanishing holds for log-canonical pairs. On the other hand, the usual statement for Kawamata-Viehweg vanishing talks about a klt pair $(X,\...
- 625
2
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1
answer
299
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Sequences of divisors satisfying Serre vanishing?
Serre's vanishing theorem (SV) states that, on a projective variety $X$ with a choice of ample line bundle $\mathcal{O}_X(1)$, for any coherent sheaf $F$, we have
$$H^i(X,F(m))=0,\quad m>>0$$
...
- 23.1k
4
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0
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Vanishing theorems on toric DM stacks
In chapter 9 of the book Toric varieties by Cox-Little-Schenck several cohomology vanishing theorems for toric varieties are proved or mentioned.
In this question I am interested in references for ...
- 23.1k
12
votes
1
answer
746
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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 ...
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1
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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 ...
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