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Results tagged with cv.complex-variables
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user 2191
Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.
15
votes
Accepted
Is the Hodge Conjecture an $\mathbb{A}^1$-homotopy invariant?
Isn't this very easy? If the varieties are $\mathbb{A}^1$-homotopy equivalent, then their Voevodsky motives are isomorphic also (since there is a connecting functor making the obvious diagram commutat …
- 16.9k
3
votes
3
answers
406
views
When can Hodge filtrations (decompositions?) be described explicitly in terms of periods?
It seems that there is no chance to explain the Hodge theory (to students) in an hour or so. Yet do there exist any cases when the Hodge filtration (or the Hodge decomposition) of the cohomology of a …
- 16.9k
20
votes
1
answer
2k
views
Any algebraic substitute for Morse theory (and homology) in arbitrary characteristic?
As far as I know, Morse theory yields much information on the topology of smooth manifolds; in particular, it can be used to prove Artin's vanishing (that the singular cohomology of smooth complex var …
- 16.9k