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Results tagged with complex-geometry
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user 25566
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.
13
votes
1
answer
2k
views
Chern classes of ideal sheaf of an analytic subset
Let $X$ be a Kähler manifold of dimension $n$, and $Z \subset X$ an analytic subset of codimension $k$. I have read in a paper the following result, a proof of which I cannot find:
$$c_k(\mathscr{I}_ …
- 365
4
votes
1
answer
3k
views
First Chern class of canonical bundle ?
This is a somewhat simple question: consider a complex manifold $M$ and its canonical bundle $\omega_X$. It is clear that in $H^2(X,\mathbb{R})$,
$$c_1(\omega_X) = - c_1(T_X)$$
(Obvious using Chern-W …
- 365
4
votes
2
answers
1k
views
Holomorphic bundles and maps to the Grassmannian ?
Hello,
In the differentiable case it is quite easy to prove that vector bundles are equivalent to smooth maps to the Grassmannian $G_{k}(\mathbb{R}^N)$ for some integer $N>>0$. The proofs I have seen …
- 365
1
vote
1
answer
808
views
Picard group of a K3 surface generated by a curve
In Lazarsfeld's article "Brill Noether Petri without degenerations" he mentions the fact that for any integer $g \geq 2$, one may find a K3 surface $X$ and a curve $C$ of genus $g$ on $X$ such that th …
- 365