All Questions
Tagged with sheaf-cohomology coherent-sheaves
10 questions with no upvoted or accepted answers
6
votes
0
answers
511
views
de Rham isomorphism with holomorphic forms
For a non-compact Riemann surface $X$ there is an isomorphism:
$$\Omega(X)/\mathrm d \mathcal O(X)\simeq H^1(X,\mathbb C)$$
where $\Omega$ is the sheaf of holomorphic forms on $X$. The group on the ...
- 81
5
votes
0
answers
268
views
Coherent cohomological dimension and affine morphisms
For simplicity, all varieties in this question are quasiprojective varieties over an algebraically closed field of characteristic $0$.
The coherent cohomological dimension $cd(X)$ of a variety $X$ is ...
- 59
4
votes
0
answers
239
views
Proper base change for non-quasicoherent sheaves
For a proper flat map $f: X \to Y$ (of reasonable schemes) and a closed embedding $i: Y' \to Y$, we know by EGA the base change quasi-isomorphism, where $f'$ and $i'$ are the pullbacks of $f$ and $i$:
...
- 2,040
4
votes
0
answers
110
views
Convolution of DQ-Modules
On page 92 of Deformation Quantization Modules Kashiwara and Schapira define two different convolution products for DQ-modules that differ by whether one uses $Rp_{13*}$ or $Rp_{13!}$ to push forward....
- 41
3
votes
0
answers
155
views
Semicontinuity of cohomology of torsion-free sheaves restricted to divisors
Let $X$ be a smooth projective variety, $\mathcal{E}$ a torsion-free coherent sheaf on $X$ and $\mathfrak{d}$ a linear system of divisors in $X$.
I would like to show (at least when $X$ is a surface) ...
- 263
2
votes
0
answers
62
views
Base change for finding fibers of the pushforward of a line bundle along a proper non-flat morphism
Let $f: X \to Y$ be a proper morphism whose fibers have different dimensions, in particular $f$ is not flat. Let $L$ be a line bundle on $X$. What conditions would be sufficient to be able to conclude ...
- 2,974
2
votes
0
answers
142
views
Computing the coherent cohomology of a quasiprojective variety
I have a quasiprojective variety given by some explicit quations. How do I compute its coherent cohomology (with coefficients in the structure sheaf)? Do I use the Cech complex for an open affine ...
- 2,974
2
votes
0
answers
306
views
Cech cohomology.
Let us consider the scheme $X$ and the coherent sheaf $\cal F$ on it. We consider finitely many affine open covers $U_{\lambda}$ with $\lambda \in \Lambda$. When I calculate Cech cohomology with $U_{\...
- 181
1
vote
0
answers
104
views
A sheaf for factorization
Let $R$ be a commutative ring with $1$ and let $X$ be the space of connected componens of $Spec (R) $ with Zariski topology ( The boolean spectrum of $R $ )and let for each $x\in X$ there exists a ...
- 11
0
votes
0
answers
186
views
Do infinitesimal neighbourhoods help to compute the inverse images of coherent sheaves?
Let $i:Z\to X$ be a closed embedding of (projective) varieties; $S$ is a coherent sheaf on $X$. How could one compute $H^*(Z,i^\ast S)$ (I don't know whether I should write $H^\ast (Z,i^{-1}S)$ ...
- 16.9k