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Results tagged with complex-geometry
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user 148020
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.
3
votes
0
answers
126
views
differential map of a flow
I am trying to understand this passage of the paper "APPLICATIONS OF THE HOLOMORPHIC LEFSCHETZ FORMULA" from Kosniowski
1) Just to make sure I understand the notion correctly: Let $n$ be the comple …
- 315
5
votes
1
answer
335
views
$h^{p,q} = h^{q,p}$ on complex smooth projective scheme
I know that for compact Kähler manifolds $M$ there is an isomorphism:
$$ H^p(M, \Omega_M^q) = H^q(M, \Omega_M^p) $$
where $\Omega_M$ is the sheaf of holomorphic $1$-forms. It is because $H^p(M, \Omega …
- 35.2k
5
votes
0
answers
701
views
Wedge product on cohomology groups
I have a complex smooth projective scheme $X$ with the sheaf of Kähler differentials $\Omega_{X/\mathbb{C}}$ (or only $\Omega$). Denote its analytification $X^{an}$ with analytification morphism $h:X^ …
- 315
5
votes
0
answers
169
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multiplication in spectral sequence
I am trying to understand this paper. Let $M$ be a compact Kaehler manifold of dimension $n$, $X$ is a holomorphic vector field, $i_X$ the contraction operator, i.e. for $\alpha$ a $p$-form, then $i_X …
- 315