All Questions
4 questions
4
votes
1
answer
382
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Formula for genus of a Fano variety
This is a simple question, just looking for a reference for a formula.
As far I understand the genus of a prime Fano $n$-fold is defined to be the genus of a complete intersection of $n-1$ smooth ...
- 6,995
2
votes
0
answers
282
views
Global Torelli and local Torelli for Fano threefolds (need reference)
It is known that in general Globally Torelli does not imply the local Torelli theorem, see
Is the Torelli map an immersion?
Globally Torelli means that the period map $\mathcal{P}$ is injective and
...
- 1,982
15
votes
2
answers
1k
views
How does one prove that the complete intersection of a quadric and a cubic of $\mathbb P^5$ is unirational?
The question is stated in the title, but I would like to add some motivation.
I've been teaching a course on complex tori and abelian varieties this semester and I would like to end it by showing ...
- 6,253
3
votes
1
answer
609
views
Semiorthogonal decompositions for Fano 3-folds and 4folds
Let $X$ be a projective Fano 3-fold or 4-fold and let $D^b(X)$ be the bounded derived category of coherent sheaves on $X$. For what $X$ is it known a semi orthogonal decomposition into indecomposable ...
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