The Picard group of the moduli space of r-Spin Riemann surfaces

Oscar Randal-Williams

doi:10.1016/j.aim.2012.04.027

The Picard group of the moduli space of r-Spin Riemann surfaces

Oscar Randal-Williams

Department of Mathematical Sciences

5 Citations (Scopus)

Abstract

An r-Spin Riemann surface is a Riemann surface equipped with a choice of rth root of the (co)tangent bundle. We give a careful construction of the moduli space (orbifold) of r-Spin Riemann surfaces, and explain how to establish a Madsen–Weiss theorem for it. This allows us to prove the “Mumford conjecture” for these moduli spaces, but more interestingly allows us to compute their algebraic Picard groups (for g≥10, or g≥9 in the 2-Spin case). We give a complete description of these Picard groups, in terms of explicitly constructed line bundles.

Original language	English
Journal	Advances in Mathematics
Volume	231
Issue number	1
Pages (from-to)	482-515
ISSN	0001-8708
DOIs	https://doi.org/10.1016/j.aim.2012.04.027
Publication status	Published - 10 Sept 2012

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10.1016/j.aim.2012.04.027

Cite this

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