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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 |
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Geometry & Topology 28 (2024) 803–866
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Abstract |
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We highlight several novel aspects of the moduli space of curves of genus , the first genus where phenomena related to surfaces no longer govern the birational geometry of . We compute the class of the nonabelian Brill–Noether divisor on 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 with slope less than . 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 is of general type. Among other things, we also prove the Bertram–Feinberg–Mukai and the strong maximal rank conjectures on . |
Keywords
strong maximal rank conjecture, genus 13, Mukai–Petri
divisor, Prym moduli space
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Mathematical Subject Classification
Primary: 14H10
Secondary: 14T20
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References |
Publication
Received: 31 October 2021
Revised: 17 February 2022
Accepted: 1 July 2022
Published: 13 March 2024
Proposed: Dan Abramovich
Seconded: Marc Levine, Mark Gross
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Authors |
| Gavril Farkas | |
| Institut für Mathematik Humboldt-Universität zu Berlin Berlin Germany |
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| David Jensen | |
| Department of Mathematics University of Kentucky Lexington, KY United States |
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| Sam Payne | |
| Department of Mathematics University of Texas at Austin Austin, TX United States |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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