Duke Mathematical Journal

Monodromy of codimension 1 subfamilies of universal curves

Richard Hain

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Abstract

Suppose that g3, that n0, and that 1. The main result is that if E is a smooth variety that dominates a codimension 1 subvariety D of Mg,n[], the moduli space of n-pointed, genus g, smooth, projective curves with a level structure, then the closure of the image of the monodromy representation π1(E,eo)Spg() has finite index in Spg(). A similar result is proved for codimension 1 families of principally polarized abelian varieties.

Article information

Source
Duke Math. J., Volume 161, Number 7 (2012), 1351-1378.

Dates
First available in Project Euclid: 4 May 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1336142078

Digital Object Identifier
doi:10.1215/00127094-1593299

Mathematical Reviews number (MathSciNet)
MR2922377

Zentralblatt MATH identifier
1260.14014

Subjects
Primary: 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14H15: Families, moduli (analytic) [See also 30F10, 32G15]
Secondary: 14F35: Homotopy theory; fundamental groups [See also 14H30] 14F45: Topological properties

Citation

Hain, Richard. Monodromy of codimension 1 subfamilies of universal curves. Duke Math. J. 161 (2012), no. 7, 1351--1378. doi:10.1215/00127094-1593299. https://projecteuclid.org/euclid.dmj/1336142078


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