Algebra & Number Theory
- Algebra Number Theory
- Volume 10, Number 9 (2016), 1935-1948.
Extremality of loci of hyperelliptic curves with marked Weierstrass points
The locus of genus-two curves with marked Weierstrass points has codimension inside the moduli space of genus-two curves with marked points, for . It is well known that the class of the closure of the divisor obtained for spans an extremal ray of the cone of effective divisor classes. We generalize this result for all : we show that the class of the closure of the locus of genus-two curves with marked Weierstrass points spans an extremal ray of the cone of effective classes of codimension , for . A related construction produces extremal nef curve classes in moduli spaces of pointed elliptic curves.
Algebra Number Theory, Volume 10, Number 9 (2016), 1935-1948.
Received: 9 November 2015
Revised: 17 June 2016
Accepted: 10 September 2016
First available in Project Euclid: 16 November 2017
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Chen, Dawei; Tarasca, Nicola. Extremality of loci of hyperelliptic curves with marked Weierstrass points. Algebra Number Theory 10 (2016), no. 9, 1935--1948. doi:10.2140/ant.2016.10.1935. https://projecteuclid.org/euclid.ant/1510842609