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Results tagged with hodge-theory
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user 3377
The study of harmonic differential forms on complex projective varieties, their invariantly defined filtrations, their integrals over topological cycles, especially over subvarieties, the deformations of these integrals and filtrations in families, and a multitude of generalizations.
8
votes
1
answer
332
views
reference to a theorem about a product of harmonic and parallel forms
Let $\alpha$ be an exterior product of a harmonic and a parallel form on a Riemannian manifold. Then $\alpha$ is known to be harmonic. I have heard that this is an old result due to R. Bott, but I cou …
- 9,237
4
votes
Accepted
Hodge isometry sending the Kahler class to its opposite
It is impossible, because the birational (movable) nef cone is mapped to birational nef cone, where birational nef cone is a cone of all classes which are non-negative on all curves which move in fami …
- 9,237
3
votes
Accepted
The Hodge number $h^{2,0}$ of (finite) quotient variety of a K3 surface
Your variety $X/G$ is an orbifold; on
a singular variety, the Hodge decomposition
does not work, but on an orbifold, it works
just as well. Then $G$ acts on $H^*(X,{\Bbb Q})$, and
$H^*(X/G,{\Bbb Q})$ …
- 9,237