All Questions
7
questions
1
vote
0
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121
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How does the Torelli theorem behave with respect to cyclic covering?
Let $Y\xrightarrow{2:1}\mathbb{P}^3$ be the double cover, branched over a quartic K3 surface $S$, known as quartic double solid. Assume $S$ is generic, we know that there is a Torelli theorem for $Y$ ...
- 1,962
3
votes
0
answers
110
views
What is the correct definition of intermediate Jacobian for this singular threefold?
I am considering blow up of $\mathcal{C}\subset(\mathbb{P}^1)^3$, $X=\operatorname{Bl}_{\mathcal{C}}(\mathbb{P}^1)^3$, where $\mathcal{C}$ is a curve given by $$\{s^2u=0\}\subset\mathbb{P}^1_{s:t}\...
- 1,962
1
vote
0
answers
140
views
Intermediate Jacobian for small resolution of a singular Fano threefold?
I am mainly interested in the nodal Gushel-Mukai threefold. Let $X$ be a Gushel-Mukai threefold with one node, then by page 21 of the paper https://arxiv.org/pdf/1004.4724.pdf there is a short exact ...
- 1,962
7
votes
1
answer
699
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Generalised Hodge Conjecture
Further to my question,
A Naive Question on Mixed Motives and Mixed Hodge Structures
that has received very good replies and suggestions, and I really appreciate it. I am going to ask a question on ...
- 2,971
8
votes
1
answer
807
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A Naive Question on Mixed Motives and Mixed Hodge Structures
As a physicist, I have some naive questions about mixed motives and its mixed Hodge structure (MHS) realization. Any references, comments, answers will be appreciated!
The category of mixed motives ...
- 2,971
0
votes
0
answers
247
views
Hodge structure of abelian surfaces
In my case, I have an abelian surface $A$ of (2,8)-polarization, and I have some finite group (may not be abelian group) $G$ acting on $A$ without fixed point. I want to understand when there is a ...
- 3,392
4
votes
0
answers
234
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Leray degeneration for smooth projective morphisms and formality of families of compact Kähler manifolds
Let $\pi \colon X \to S$ be a smooth projective morphism of algebraic varieties, say over $\mathbf C$. By Deligne's argument ("Théorème de Lefschetz...", 1968), there is for each $i$ an injection
$$ \...
- 39.5k