Extremality of Rational Tails Boundary Strata in ${\overline{\mathcal{M}}}_{g,n}$

Abstract

We review and develop some techniques used to investigate the effective cones of higher codimension classes. Our results show that a large collection of boundary strata of rational tails type are extremal in their effective cones on ${\overline{\mathcal{M}}}_{g,n}$ and provide evidence for the conjecture that all boundary strata of ${\overline{\mathcal{M}}}_{g,n}$ are extremal. As a corollary, we show that all boundary strata are extremal in genus zero.

Significant corrections made throughout; main results weakened; auxiliary results added

References in corpus (3)

• Extremal higher codimension cycles on moduli spaces of curves
• Hyperelliptic classes are rigid and extremal in genus two
• An extremal effective survey about extremal effective cycles in moduli spaces of curves

Cited by in corpus (1)

• On the cone of effective surfaces on ${\overline{\mathcal{A}}}_3$