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Results tagged with complex-geometry
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user 115211
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.
11
votes
Algebraic vs analytic normality
Francesco Polizzi's answer is perfectly fine, but let me try to explain the technique which helps to relate a lot of "local" properties of locally finite type schemes over $\mathbf C$ to their counter …
- 2,841
2
votes
Accepted
Hodge decomposition of the symmetric product of a curve
Look at Example $1.1$ in this paper for a nice formula.
You can also compute them by hands (and, hopefully, prove the desired formula) by identifying $\mathrm{H}^{p,q}(\operatorname{Sym}^n X)$ with …
- 2,841
9
votes
Hodge decomposition and degeneration of the spectral sequence
I am far from being an expert in this area, but I will try to present my understanding of this subject.
First of all, this is true that Hodge decomposition holds for smooth proper varieties over $\m …
- 2,841
3
votes
1
answer
398
views
Decomposition theorem over more general base schemes
The BBDG decomposition theorem says that if $f\colon X \to Y$ is a projective morphism of finite type $\mathbf{C}$-schemes and $X$ is smooth of (pure) dimension $d$ then $\mathbf{R}f_*\mathbf{Q}_\ell[ …
- 2,841