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15 February 2007 Hecke correspondence, stable maps, and the Kirwan desingularization
Young-Hoon Kiem
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Duke Math. J. 136(3): 585-618 (15 February 2007). DOI: 10.1215/S0012-7094-07-13636-6

Abstract

We prove that the moduli space M̲0,0(N,2) of stable maps of degree 2 to the moduli space N of rank 2 stable bundles of fixed odd determinant OX(-x) over a smooth projective curve X of genus g3 has two irreducible components that intersect transversely. One of them is Kirwan's partial desingularization M~X of the moduli space MX of rank 2 semistable bundles with determinant isomorphic to OX(y-x) for some yX. The other component is the partial desingularization of the geometric invariant theory (GIT) quotient PHom(sl(2),W)//PGL(2) for a vector bundle W=R1π*L-2(-x) 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 M̲0,0(N,2) are related by explicit contractions

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Young-Hoon Kiem. "Hecke correspondence, stable maps, and the Kirwan desingularization." Duke Math. J. 136 (3) 585 - 618, 15 February 2007. https://doi.org/10.1215/S0012-7094-07-13636-6

Information

Published: 15 February 2007
First available in Project Euclid: 29 January 2007

zbMATH: 1119.14033
MathSciNet: MR2309175
Digital Object Identifier: 10.1215/S0012-7094-07-13636-6

Subjects:
Primary: 14D20 , 14H60
Secondary: 14E15

Rights: Copyright © 2007 Duke University Press

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Vol.136 • No. 3 • 15 February 2007
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