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Results tagged with complex-geometry
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user 8003
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
Accepted
A very general complex torus is simple
I think yes. Let $J$ be the complex structure on $\mathbb{R}^{2g}$. Let $L$ be the lattice. Then there is a complex subtorus if and only if $L$ intersects some complex-linear subspace in a full sub-la …
- 1,493
3
votes
Accepted
Loci in the moduli space of K3 surfaces associated to lattices
I won't completely answer your question, but will try to just rephrase it in a certain way. You are asking when two given moduli spaces of lattice-polarized K3 surfaces $M_L$ and $M_{L'}$ intersect. T …
- 1,493
5
votes
1
answer
337
views
Quotient of a smooth projective surface by an involution
Is the quotient of a smooth complex projective surface by an involution projective? Suppose the quotient happens to be smooth; does that change the situation?
- 1,493
1
vote
Toroidal embedding
naf's comment is correct. This example can be seen as an instance of Mumford's construction of degenerations of abelian varieties into unions of toric varieties. Here is a "purely toric" construction …
- 1,493
6
votes
Examples of non-Kähler compact complex manifolds which satisfy the Dolbeault isomorphism
I am slightly confused by Francesco's comment and answer, because the Frolicher spectral sequence does degenerate for compact complex surfaces. So why isn't a non-Kahler surface an example? Perhaps th …
- 1,493
2
votes
0
answers
147
views
Open Period Integrals of Elliptically Fibered K3 surfaces
Let M be the period domain for elliptic K3 surfaces $(X,\Omega)$ with a holomorphic two-form. Denote the fiber class $f$. Then $$M=\{\Omega\in f^\perp\otimes \mathbb{C}\,:\, \Omega\cdot \Omega=0, \,\O …
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