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Results tagged with hodge-theory
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user 3545
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.
15
votes
1
answer
722
views
Semistable filtered vector spaces, a Tannakian category.
Let $k$ be a field (char = 0, perhaps). Let $(V,F)$ be a pair, where $V$ is a finite-dimensional $k$-vector space, and $F$ is a filtration of $V$, indexed by rational numbers, satisfying:
$F^i V \ …
- 13.3k
6
votes
Accepted
Exercises in Hodge Theory
One suggestion: "Period mappings and Period Domains", by Carlson, Muller-Stach, and Peters, in the Cambridge studies in advanced mathematics series. It's a very nice read, and each chapter comes wit …
- 13.3k
7
votes
Accepted
When is a homogeneous space a variety?
I'll try to answer both questions, though I will change the first question somewhat. Let's work in the setting of a real reductive algebraic group $G$ and a closed subgroup $H \subset G$.
Your fir …
- 13.3k