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Tagged with hodge-structure reference-request
4 questions
8
votes
1
answer
980
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Variations of Hodge structures over the line
Let $f\colon X\to \mathbb{A}^1$ be a smooth projective morphism of complex algebraic manifolds, where the target $\mathbb{A}^1$ is the affine line. Are there any restrictions on the Hodge structures ...
6
votes
1
answer
434
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Mixed Hodge structure and cup product
I'm looking for a reference for the answer to the following questions.
Let $X$ be an algebraic variety over C. When is the cup product a morphism of Mixed Hodge structures? Does $X$ have to be smooth?...
3
votes
0
answers
116
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Is the category of pure Hodge structures abelian semi-simple? [duplicate]
Apologies if the question in the title is too elementary.
A reference would be helpful.
3
votes
0
answers
982
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Reference for the Hodge polynomial or the Hodge Characteristic
What is the first work that studies, refers to, or mentions the Hodge characteristic?
The Hodge polynomial is the unique ring homomorphism
$$
P_{hdg}:K_0(\mathbf{Var}/\mathbb{C)}\to \mathbb{Z}[u,v,u^{...