All Questions
61 questions
2
votes
0
answers
151
views
Moduli space of sheaves on a ribbon
In the paper "A non-linear deformation of the Hitchin dinamycal system", Donagi-Ein-Lazarsfeld describe the irreducible components of the moduli space $\mathcal M_R$ of stable sheaves of numerical ...
- 453
2
votes
1
answer
168
views
stable vector bundle and space surves
I am sure this is well known, but I am not an expert...so I appreciate any help
Let $C \subset \mathbb{P}^3$ be the complete intersection of two hypersurfaces of degree $d_1$ and $d_2$. Let $U_{d_1,...
- 21
1
vote
2
answers
913
views
Connections on the Hodge bundle?
Let $\mathcal{M}_g$ be the moduli space of curves of genus $g$. Consider the holomorphic bundle $\mathcal{H}^k\rightarrow\mathcal{M}_g$ whose fiber over a curve $C\in\mathcal{M}_g$ is the space of ...
- 1,804
2
votes
2
answers
998
views
Is the moduli space of stable vector bundles over a smooth projective curve fano?
Let $K$ be a field of characteristic zero but not algebraically closed. Let $C$ be a smooth projective curve over $K$. Let $r, d$ be two positive integers that are coprime. Consider the moduli space ...
- 1,593
4
votes
0
answers
486
views
Stack of vector bundles (on a curve) over a strictly semi-stable point of the moduli space
Consider the stack $Bun_{r,d}^{ss}$ of rank $r$ semi-stable vector bundle of degree $d$ over a fixed curve. There exists also a coarse moduli space $M$ built via GIT. Over the stable locus of $M$ it ...
- 3,779
14
votes
0
answers
2k
views
conformal blocks for beginners
I have given now a couple of talks that involve conformal blocks bundles on the moduli stack $\overline{\mathcal{M}}_{g,n}$, in front of a public of algebraic geometers but not specialists of the ...
- 3,779
2
votes
1
answer
765
views
fano moduli varieties of vector bundles
Let $M$ be a fine moduli space of vector bundles on curve which is an algebraic variety as well. The first example of such an object that I have in mind is rank 2, deg 1 VB on a genus 2 curve. This is ...
- 3,779
3
votes
1
answer
610
views
moduli of vector bundles on a surface
Let $S$ be a smooth projective surface with an ample divisor $X\subset S$. Consider the
moduli stack of vector bundles $F$ on $S$ such that
1) $c_1(F)=0$
2) $c_2(F)=n$
3) The restriction of $F$ to $...
- 7,037
9
votes
2
answers
4k
views
Reference request: moduli spaces of vector bundles
I am trying to study the moduli spaces of holomorphic vector bundles quickly, and I'm primarily interested in understanding:
Why and where the stability condition is used.
How are the moduli spaces ...
61
votes
11
answers
21k
views
What are some open problems in algebraic geometry?
What are the open big problems in algebraic geometry and vector bundles?
More specifically, I would like to know what are interesting problems related to moduli spaces of vector bundles over ...
9
votes
6
answers
3k
views
Reference request: Moduli spaces of bundles over singular curves
I would like to know some reference (articles, books...) about any kind of moduli spaces of any of the following objects:
vector bundles
torsion-free sheaves
principal bundles
parabolic bundles
over ...