Questions tagged [fano-varieties]
The fano-varieties tag has no usage guidance.
106 questions
11
votes
0
answers
684
views
Big tangent bundle
Let $X$ be a nonsingular complex algebraic variety whose tangent bundle is $T_X$. I use Lazarsfeld's book for the definition of a big vector bundle. A line bundle $L$ is big if it has Itaka dimension ...
- 11.6k
7
votes
1
answer
609
views
Is there an Enriques–Kodaira-like classification of Fano threefolds?
I am mainly interested in varieties over an algebraic closed field $k$ (or $\mathbb{C}$). The classification of complex surface is established in the last century and known as Enriques–Kodaira ...
- 11.6k
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 ...
- 66.3k
14
votes
1
answer
1k
views
Frobenius splitting of Fano varieties
Dear MO,
Question 1. Do you know of an example of a Fano variety which is not Frobenius split?
Background
(1) A variety $X$ in characteristic $p$ is called Frobenius split if there is a "$p$-th ...
CommunityBot
- 1
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 ...
- 39.3k
6
votes
0
answers
378
views
Bound for the Picard number of a Fano 3-fold
Let $X$ be a Fano 3-fold with terminal singularities. Is there some bound (possibly explicit) for the Picard rank of $X$ ?
If $X$ is smooth, it is well-known that the bound is $10$, obtained by del ...
- 7,722