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Results tagged with complex-geometry
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user 56878
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.
1
vote
1
answer
958
views
Torsion in the (co-)homology of a smooth projective variety - what is known in general?
There are lots of ways in which the complex singular (co-)homology of a smooth projective variety over $\mathbb{C}$ is "special" among complex manifolds - the hard Lefschetz theorem, the Hodge decompo …
- 3,058
6
votes
1
answer
2k
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Algebraic vs. homological equivalence for curves on a smooth complex projective surface
Let $X$ be a smooth projective surface over $\mathbb{C}$. Then there is the exponential sheaf sequence:
$$
0 \rightarrow \mathbb{Z} \rightarrow \mathscr{O}_X \rightarrow \mathscr{O}_X^\times \rightarr …
- 3,058