ℛ15 is of general type

Bruns, Gregor

doi:10.2140/ant.2016.10.1949

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$\overline{\mathscr{R}}_{15}$ is of general type

Gregor Bruns

Vol. 10 (2016), No. 9, 1949–1964

DOI: 10.2140/ant.2016.10.1949

Abstract

We prove that the moduli space ${\bar{ℛ}}_{15}$ of Prym curves of genus $15$ is of general type. To this end we exhibit a virtual divisor ${\bar{D}}_{15}$ on ${\bar{ℛ}}_{15}$ as the degeneracy locus of a globalized multiplication map of sections of line bundles. We then proceed to show that this locus is indeed of codimension one and calculate its class. Using this class, we can conclude that $K_{{\bar{ℛ}}_{15}}$ is big. This complements a 2010 result of Farkas and Ludwig: now the spaces ${\bar{ℛ}}_{g}$ are known to be of general type for $g \geq 14$ .

Keywords

Prym variety, Kodaira dimension, genus 15 curve, moduli space

Mathematical Subject Classification 2010

Primary: 14H10

Secondary: 14E08, 14H40, 14K10

Milestones

Received: 18 December 2015

Revised: 19 April 2016

Accepted: 30 August 2016

Published: 22 November 2016

Authors

Gregor Bruns
Humboldt-Universität zu Berlin Unter den Linden 6 D-10099 Berlin Germany

Vol. 10, No. 9, 2016