Alternate Compactifications of Moduli Spaces of Curves

Abstract

We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber decompositions of $\M_{g,n}$.

86 pages. Revised version. Submitted to Handbook of Moduli, Farkas and Morrison, eds

References in corpus (17)

• Good moduli spaces for Artin stacks
• Log minimal model program for the moduli space of stable curves: The first flip
• Numerical criteria for divisors on $\M_{g}$ to be ample
• Moduli spaces of curves with linear series and the slope conjecture
• Singularities with G_m-action and the log minimal model program for ${\bar{M}}_g$
• Fulton's Conjecture for \bar{M}_{0,7}
• Adjoint rings are finitely generated
• Towards a classification of modular compactifications of the moduli space of curves
• Ample divisors on moduli spaces of weighted pointed rational curves, with applications to log MMP for ${\bar{M}}_{0,n}$
• Modular compactifications of M_{1,n}
• The universal Whitham hierarchy and the geometry of the moduli space of pointed Riemann surfaces
• GIT Constructions of Moduli Spaces of Stable Curves and Maps
• Covers of the projective line and the moduli space of quadratic differentials
• Groebner techniques for low degree Hilbert stability
• Moduli spaces of hyperelliptic curves with A and D singularities
• On the universal abelian variety of dimension 4
• Moduli spaces of weighted stable curves and log canonical models of ${\bar{M}}_{g,n}$

Cited by in corpus (15)

• On the structure of instability in moduli theory
• Finite Hilbert stability of (bi)canonical curves
• GIT for polarized curves
• Stable log surfaces, admissible covers, and canonical curves of genus 4
• GIT Constructions of Log Canonical Models of M_g
• The final log canonical model of the moduli space of stable curves of genus four
• Log canonical models and variation of GIT for genus four canonical curves
• GIT and moduli with a twist
• Stability of genus five canonical curves
• An outline of the log minimal model program for the moduli space of curves
• On some modular contractions of the moduli space of stable pointed curves
• On GIT quotients of Hilbert and Chow schemes of curves
• On Chow Stability for algebraic curves
• Log canonical models for ${\bar{M}}_{g,n}$
• Mori's program for ${\bar{M}}_{0,6}$ with symmetric divisors