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Results tagged with complex-geometry
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user 4437
Complex geometry is the study of complex manifolds, complex algebraic varieties, complex analytic spaces, and, by extension, of almost complex structures. It is a part of differential geometry, algebraic geometry and analytic geometry.
5
votes
2
answers
2k
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the central issues in complex geometry
I want to know about people in researching complex (maybe differential) geometry are careing about what currently ? For example ,$L^2$ estimate inspired by Lars Hormander is a very useful tool,and how …
- 399
0
votes
Accepted
how to prove the relationship between pseudoconvexity and the monge-ampere matrix?
Since $\phi$ is always nonzero inside $\Omega$ , so this matrix has precise one negative eigenvalue and n positive eigenvalues is equivalent to $-\partial\bar{\partial}log\phi$ is non-negative , but w …
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1
vote
1
answer
315
views
how to prove the relationship between pseudoconvexity and the monge-ampere matrix?
In several complex variables , to determine the pseudoconvexity of a domain in $C^n$ is very important . There are various criterion to decide whether a domain is pseudoconvex . In particular ,if th …
- 399
6
votes
1
answer
3k
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what is the motivation of Shimura variety?
Tonight, a friend of mine give me a concise introduction to Shimura variety . I only get some first impression of it. I think the hodge structure is a generalization of the cohomology ring of Kaehler …
- 399
3
votes
2
answers
1k
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who can give me a example of coherent sheaf
What are examples of coherent sheaves $\mathfrak{F}$ on a compact complex $n$-fold with $\dim \operatorname{Supp} \mathfrak{F}=p$ , where $0\leq p \leq n$ ? And how can they be described in local coor …
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1
vote
1
answer
407
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how to prove the following fact in sheaf cohomology ?
Let $X$ be a compact complex n-fold . Then for every coherent sheaf $\mathfrak{F}$ on $X$ , and every holomorphic line bundle $L$ on $X$ , then the dimension of $H^0 (X,\mathfrak{F}\otimes\mathcal{O}_ …
- 399
2
votes
1
answer
446
views
flatness of coherent analytic sheaf
I meet a problem like this : given a short exact sequence $0\rightarrow E_1\rightarrow E_2\rightarrow E_3\rightarrow 0$ , where $E_i,i=1,2,3$ are coherent sheaves over a compact complex manifold $X$ . …
- 399
2
votes
0
answers
324
views
Is there asymptotic expansion of heat kernel of complex laplacian?
On real Riemannian manifold , the heat kernel of the laplacian have an asymptotic expansion . But on complex manifold , i haven't seen a result like this , i.e. the heat kernel of the Kodaira Laplacia …
- 399