Hecke Correspondence, Stable Maps and the Kirwan Desingularization
代数几何
2007-05-23 v1
摘要
We prove that the moduli space of stable maps of degree 2 to the moduli space of rank 2 stable bundles of fixed determinant O(-x) over a smooth projective curve of genus g>2 has two irre- ducible components which intersect transversely. One of them is Kir- wan's partial desingularization of the moduli space of rank 2 semistable bundles with determinant isomorphic to O(y-x) for some y in X. The other component is the partial desingularization of PHom(sl(2)^*;W)//PGL(2) for a vector bundle W of rank g over the Jacobian of X. We also show that the Hilbert scheme H, the Chow scheme C of conics in N and the moduli space of stable maps of degree 2 are related by explicit contractions.
引用
@article{arxiv.math/0512005,
title = {Hecke Correspondence, Stable Maps and the Kirwan Desingularization},
author = {Young-Hoon Kiem},
journal= {arXiv preprint arXiv:math/0512005},
year = {2007}
}