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Results tagged with complex-geometry
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user 4008
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.
16
votes
Accepted
Projective variety with no syzygies but not isomorphic to projective space
The answer is no. Take any projective manifold $X$ mapping $\pi\colon
X\rightarrow\mathbb P^n$ to such that $\pi_*\mathcal O_X=\mathcal O_{\mathbb
P^n}$ and let $L$ be $\pi^*\mathcal O(1)$. Then $H^ …
- 22.6k
11
votes
Accepted
Can a non-algebraic complex manifold be embedded meromorphically into projective space?
If $X$ is not compact there are loads of problems so I follow you in adding compactness as a condition.
Under the assumption of the question $X$ is bimeromorphic to a projective variety and hence by …
- 22.6k
8
votes
Holomorphic vector fields acting on Dolbeault cohomology
These are comments on Dmitri's answer.
I don't think the surface example can work as all holomorphic forms on a compact
surface are closed (a result due to Kodaira I believe). The Cartan formula $L_v …
- 22.6k
7
votes
Deformations of sheaves via automorphisms. How to express $Ext^1$?
Here is a not so fancy description.
There is a general principle (in algebraic geometry but applicable to some
neighbouring disciplines) that says that anything that is functorial and
commutes with b …
- 22.6k