Algebra & Number Theory

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

Gregor Bruns

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We prove that the moduli space ¯15 of Prym curves of genus 15 is of general type. To this end we exhibit a virtual divisor D¯15 on ¯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 ¯ 15 is big. This complements a 2010 result of Farkas and Ludwig: now the spaces ¯g are known to be of general type for g 14.

Article information

Algebra Number Theory, Volume 10, Number 9 (2016), 1949-1964.

Received: 18 December 2015
Revised: 19 April 2016
Accepted: 30 August 2016
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H10: Families, moduli (algebraic)
Secondary: 14E08: Rationality questions [See also 14M20] 14H40: Jacobians, Prym varieties [See also 32G20] 14K10: Algebraic moduli, classification [See also 11G15]

Prym variety Kodaira dimension genus 15 curve moduli space


Bruns, Gregor. $\overline{\mathscr{R}}_{15}$ is of general type. Algebra Number Theory 10 (2016), no. 9, 1949--1964. doi:10.2140/ant.2016.10.1949.

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