Vol. 10, No. 9, 2016

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Extremality of loci of hyperelliptic curves with marked Weierstrass points

Dawei Chen and Nicola Tarasca

Vol. 10 (2016), No. 9, 1935–1948
DOI: 10.2140/ant.2016.10.1935
Abstract

The locus of genus-two curves with $n$ marked Weierstrass points has codimension $n$ inside the moduli space of genus-two curves with $n$ marked points, for $n\le 6$. It is well known that the class of the closure of the divisor obtained for $n=1$ spans an extremal ray of the cone of effective divisor classes. We generalize this result for all $n$: we show that the class of the closure of the locus of genus-two curves with $n$ marked Weierstrass points spans an extremal ray of the cone of effective classes of codimension $n$, for $n\le 6$. A related construction produces extremal nef curve classes in moduli spaces of pointed elliptic curves.

Keywords
subvarieties of moduli spaces of curves, effective cones, higher codimensional cycles
Primary: 14H99
Secondary: 14C99
Milestones
Revised: 17 June 2016
Accepted: 10 September 2016
Published: 22 November 2016
Authors
 Dawei Chen Department of Mathematics Boston College Maloney Hall 140 Commonwealth Ave Chestnut Hill, MA 02467-3806 United States Nicola Tarasca Department of Mathematics University of Utah 155 S 1400 E Salt Lake City, UT 84112 United States