Download this article
 Download this article For screen
For printing
Recent Issues

Volume 28
Issue 2, 497–1003
Issue 1, 1–496

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
The nonabelian Brill–Noether divisor on $\overline{\mathcal{M}}_{13}$ and the Kodaira dimension of $\overline{\mathcal{R}}_{13}$

Gavril Farkas, David Jensen and Sam Payne

Geometry & Topology 28 (2024) 803–866

We highlight several novel aspects of the moduli space of curves of genus 13, the first genus g where phenomena related to K3 surfaces no longer govern the birational geometry of ¯g. We compute the class of the nonabelian Brill–Noether divisor on ¯13 of curves that have a stable rank-two vector bundle with canonical determinant and many sections. This provides the first example of an effective divisor on  ¯g with slope less than 6 + 10g. Earlier work on the slope conjecture suggested that such divisors may not exist. The main geometric application of our result is a proof that the Prym moduli space ¯13 is of general type. Among other things, we also prove the Bertram–Feinberg–Mukai and the strong maximal rank conjectures on ¯13.

strong maximal rank conjecture, genus 13, Mukai–Petri divisor, Prym moduli space
Mathematical Subject Classification
Primary: 14H10
Secondary: 14T20
Received: 31 October 2021
Revised: 17 February 2022
Accepted: 1 July 2022
Published: 13 March 2024
Proposed: Dan Abramovich
Seconded: Marc Levine, Mark Gross
Gavril Farkas
Institut für Mathematik
Humboldt-Universität zu Berlin
David Jensen
Department of Mathematics
University of Kentucky
Lexington, KY
United States
Sam Payne
Department of Mathematics
University of Texas at Austin
Austin, TX
United States

Open Access made possible by participating institutions via Subscribe to Open.