Hyperelliptic classes are rigid and extremal in genus two

Abstract

We show that the class of the locus of hyperelliptic curves with $\ell$ marked Weierstrass points, $m$ marked conjugate pairs of points, and $n$ free marked points is rigid and extremal in the cone of effective codimension-($\ell +m$) classes on ${\overline{\mathcal{M}}}_{2,\ell +2m+n}$. This generalizes work of Chen and Tarasca and establishes an infinite family of rigid and extremal classes in arbitrarily-high codimension.

Published version

References in corpus (4)

• ${\overline{M}}_{0,n}$ is not a Mori Dream Space
• On blowing up the weighted projective plane
• Extremal higher codimension cycles on moduli spaces of curves
• On the effective cone of ${\overline{\mathcal{M}}}_{g,n}$

Cited by in corpus (2)

• An extremal effective survey about extremal effective cycles in moduli spaces of curves
• Extremality of Rational Tails Boundary Strata in ${\overline{\mathcal{M}}}_{g,n}$