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

TL;DR

This paper demonstrates that Hassett's weighted stable pointed curves spaces are log canonical models of Deligne-Mumford spaces, utilizing Kollár's semipositivity to identify nef and ample divisors.

Contribution

It establishes the log canonical model relationship between Hassett's spaces and Deligne-Mumford spaces, introducing new nef and ample divisors via Kollár's semipositivity.

Findings

Hassett's spaces are log canonical models of eligne-Mumford spaces.

Construction of nef and ample tautological divisors on Hassett's spaces.

Application of Kollár's semipositivity results to moduli space geometry.

Abstract

Using Koll\'ar'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.