Effective divisors on moduli spaces of curves and abelian varieties

Abstract

This paper is an expository survey of results about the effective divisors on moduli spaces, with a focus on what is known about the effective cones of moduli spaces of stable curves and of principally polarized abelian varieties. This version incorporates clarifications and suggestions of Ana-Maria Castravet and the referee, both of whom we thank. To appear in the proceedings of the conference, "Joe at 60:A Celebration of Algebraic Geometry" edited by Brendan Hassett, James McKernan, Jason Starr and Ravi Vakil.

42 pages, 5 figures

References in corpus (15)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• The final log canonical model of the moduli space of stable curves of genus four
• Towards Mori's program for the moduli space of stable maps
• Linear sections of the Severi variety and moduli of curves
• Non-varying sums of Lyapunov exponents of Abelian differentials in low genus
• Moduli of theta-characteristics via Nikulin surfaces
• Singularities of theta divisors and the geometry of A_5
• Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on ${\bar{\mathcal{M}}}_g$
• Rational Fibrations of ${\bar{M}}_{5,1}$ and ${\bar{M}}_{6,1}$
• The Geometry of Stable Quotients in Genus One
• A note on the Petri loci
• Log Minimal Model Program for the Kontsevich Space of Stable Maps ${\bar{\mathcal{M}}}_{0,0}({\mathbb{P}}^3,3)$
• Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture
• The Gieseker-Petri divisor in M_g for genus g<=13
• Syzygies of curves and the effective cone of \bar{M}_g

Cited by in corpus (3)

• Teichmüller dynamics in the eyes of an algebraic geometer
• Recent Developments in Brill-Noether Theory
• A note on Harris Morrison sweeping families of maximal gonality