GIT Constructions of Log Canonical Models of M_g

Abstract

The purpose of this article is to give an overview of the construction of moduli spaces of curves from the viewpoint of the log minimal model program for M_g by providing an update of recent developments and discussing future problems. This survey is distinguished from the recent articles of Fedorchuk-Smyth and Morrison in its focus on low degree Hilbert stability of curves.

23 pages

References in corpus (5)

• Log minimal model program for the moduli space of stable curves: The first flip
• Alternate Compactifications of Moduli Spaces of Curves
• Singularities with G_m-action and the log minimal model program for ${\bar{M}}_g$
• Groebner techniques for low degree Hilbert stability
• An outline of the log minimal model program for the moduli space of curves

Cited by in corpus (5)

• GIT for polarized curves
• Log canonical models and variation of GIT for genus four canonical curves
• GIT and moduli with a twist
• On GIT quotients of Hilbert and Chow schemes of curves
• On Chow Stability for algebraic curves