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15 March 2012 The Picard group of the moduli space of curves with level structures
Andrew Putman
Duke Math. J. 161(4): 623-674 (15 March 2012). DOI: 10.1215/00127094-1548362

Abstract

For 4L and g large, we calculate the integral Picard groups of the moduli spaces of curves and principally polarized abelian varieties with level L structures. In particular, we determine the divisibility properties of the standard line bundles over these moduli spaces, and we calculate the second integral cohomology group of the level L subgroup of the mapping class group. (In a previous paper, the author determined this rationally.) This entails calculating the abelianization of the level L subgroup of the mapping class group, generalizing previous results of Perron, Sato, and the author. Finally, along the way we calculate the first homology group of Sp2g(Z/L) with coefficients in the adjoint representation.

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Andrew Putman. "The Picard group of the moduli space of curves with level structures." Duke Math. J. 161 (4) 623 - 674, 15 March 2012. https://doi.org/10.1215/00127094-1548362

Information

Published: 15 March 2012
First available in Project Euclid: 1 March 2012

zbMATH: 1241.30015
MathSciNet: MR2891531
Digital Object Identifier: 10.1215/00127094-1548362

Subjects:
Primary: 32G15
Secondary: 11G15, 14D22, 57N05, 57S05

Rights: Copyright © 2012 Duke University Press

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Vol.161 • No. 4 • 15 March 2012
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