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Results tagged with complex-geometry
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user 2555
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
0
answers
189
views
Real structure in the mixed Hodge structure associated to an isolated singularity
We know that a mixed Hodge structure on a complex vector space $H$ with an integral lattice $H_{\mathbb Z}$ consists of the weight filtration and the Hodge filtration. For an isolated hypersurface sin …
- 1,207
16
votes
Accepted
chern connection vs levi-civita connection
You need a non-Kahler complex manifold. Then the Chern connection will have nontrivial torsion. And the torsion corresponds to the non-closed Kahler form of the metric.
- 1,207
5
votes
3
answers
2k
views
K3 surface of genus 8
Let $V$ be a complex vector space of dimension 6 and let $G\subset {\mathbb P}^{14}\simeq {\mathbb P}(\Lambda^2V)$ be the image of the Plucker embedding of the Grassmannian $Gr(2, V)$.
Why the degre …
- 1,207