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Hecke Correspondence, Stable Maps and the Kirwan Desingularization

Young-Hoon Kiem
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Abstract

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.

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Young-Hoon Kiem. 2005-12-01. Hecke Correspondence, Stable Maps and the Kirwan Desingularization. https://arxiv.org/abs/math/0512005

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