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

Institut for Matematiske Fag

5 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Advances in Mathematics
Vol/bind	231
Udgave nummer	1
Sider (fra-til)	482-515
ISSN	0001-8708
DOI	https://doi.org/10.1016/j.aim.2012.04.027
Status	Udgivet - 10 sep. 2012

Adgang til dokumentet

10.1016/j.aim.2012.04.027

Citationsformater

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