All Questions
Tagged with fano-varieties moduli-spaces
11 questions
11
votes
2
answers
760
views
Families of Fano varieties over non-hyperbolic curves
Let $C$ be a non-hyperbolic (smooth quasi-projective connected complex algebraic) curve. That is, $C$ is isomorphic to $\mathbb P^1, \mathbb A^1, \mathbb G_m$, or an elliptic curve.
Let $f:X\to C$ be ...
- 9,497
3
votes
1
answer
449
views
Components of Kontsevich moduli space of stable maps and multiple covers
Let $X\subset \mathbb P^n$ be a smooth projective variety over $\mathbb C$ which is Fano and $M_{0,0}(X,e)$ the (projective) Kontsevich moduli space of rational cuves of degree $e>1$. Is it ...
- 69
2
votes
1
answer
353
views
Cohomology of normal bundle and tangent bundle on Gushel-Mukai threefold
Let $X$ be a smooth general ordinary Gushel-Mukai threefold. There is an embedding $X\rightarrow\mathrm{Gr}(2,5):=G$. Consider the normal bundle $\mathcal{N}_{X|G}$, how to compute cohomology of this ...
- 1,982
2
votes
0
answers
75
views
What is happening on the second step of left mutation?
Let $X$ be a smooth Gushel-Mukai fourfold, whose semi-orthogonal decomposition is given by
$$D^b(X)=\langle\mathcal{K}u(X),\mathcal{O}_X,\mathcal{U}^{\vee}_X,\mathcal{O}_X(H),\mathcal{U}^{\vee}(H)\...
- 1,982
2
votes
0
answers
144
views
Fundamental group of the moduli space of parabolic bundles with fixed determinant
I am looking for the fundamental group of the moduli space of parabolic bundles with fixed determinant over a smooth projective curve.
I know that the fundamental group of the moduli space of vector ...
- 195
2
votes
0
answers
154
views
Normal bundle of a Fano threefold as Brill-Noether loci
Let $X$ be a degree 12 or degree 16 index one prime Fano threefold. In the paper of Mukai https://arxiv.org/pdf/math/0304303.pdf page 500, Theorem 4 and Theorem 5. He said $X_{12}$ has two ambient ...
- 1,982
2
votes
0
answers
164
views
Conics on Gushel-Mukai fourfold
Let $X$ be a very general Gushel-Mukai fourfold, let $\mathcal{U}$ be the tautological sub-bundle and $\mathcal{Q}$ be the tautological quotient bundle. Let $C\subset X$ be a $\rho$-conic, then $\...
- 1,982
2
votes
0
answers
276
views
Components of Kontsevich moduli space of stable maps and reducible curves
Let $X\subset \mathbb P^n$ be a smooth projective variety which is Fano and $M_{0,0}(X,e)$ the (projective) Kontsevich moduli space of rational curves of degree $e>1$. Is it possible (or are there ...
- 69
1
vote
0
answers
101
views
Intersection of two quadrics as moduli space
Let $Y:=Q_1\cap Q_2\subset\mathbb{P}^{n-1}$ be smooth complete intersection of two quadrics. If $n$ is even, then it admits a semi-orthogonal decomposition:
$$D^b(Y)=\langle D^b(C),\mathcal{O}_Y,\...
- 1,982
1
vote
0
answers
73
views
Action of involution on instanton bundle
Let $Y$ be a quartic double solid and $E$ be an rank two instanton bundle on $Y$. By Serre's correspondence, it is not hard to show that $E$ fits into the following short exact sequence $0\rightarrow\...
- 1,982
1
vote
0
answers
25
views
The uniqueness of some semistable torsion free sheaves on Fano threefold
Let $X$ be a prime Fano threefold of index one and even genus $g\geq 6$, one can show that the moduli space of torsion free semistable sheaves $M(2,1,m_g)$ with $m_g=\left \lceil{\frac{g+2}{2}}\right \...
- 1,982