Vol. 10, No. 9, 2016

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ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
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 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 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
Mathematical Subject Classification 2010
Primary: 14H99
Secondary: 14C99
Milestones
Received: 9 November 2015
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