Moduli spaces of weighted stable curves and log canonical models of ${\bar{M}}_{g,n}$

Abstract

Using Kollár's semipositivity results, we produce a number of nef and ample tautological divisors on Hassett's spaces of weighted stable pointed curves. As an application, we prove that Hassett's spaces are log canonical models of Deligne-Mumford spaces of stable pointed curves.

A connection with Kollár's semipositivity results is explicated. Added a section showing that the GIT cone of Alexeev-Swinarski is contained in the cone of nef tautological divisors

References in corpus (3)

• Contractible Extremal Rays on \overline{M}_{0,n}
• On Log Canonical Models of the Moduli Space of Stable Pointed Curves
• Ample divisors on moduli spaces of weighted pointed rational curves, with applications to log MMP for ${\bar{M}}_{0,n}$

Cited by in corpus (4)

• Alternate Compactifications of Moduli Spaces of Curves
• Moduli spaces of hyperelliptic curves with A and D singularities
• Log canonical models for the moduli space of pointed stable rational curves
• Mori's program for the moduli space of pointed stable rational curves