Birational aspects of the geometry of M_g

Abstract

We discuss topics on the geometry of the moduli space of curves. We present a short proof of the Harris-Mumford theorem on the Kodaira dimension of the moduli space which replaces the computations on the stack of admissible covers by a simple study of tautological Koszul bundles on M_g. We also present a streamlined self-contained account of Verra's recent work on the unirationality of M_g. Finally, we discuss a proof that the moduli space of curves of genus 22 is of general type. Written for Surveys in Differential Geometry.

45 pages. Numerous minor corrections, more details on the proof that M_{22} is of general type. A new section on lower bounds on slopes of M_g

References in corpus (8)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Moduli spaces of curves with linear series and the slope conjecture
• Descendent bounds for effective divisors on the moduli space of curves
• On the universal abelian variety of dimension 4
• Covers of Elliptic Curves and the Lower Bound for Slopes of Effective Divisors on ${\bar{\mathcal{M}}}_g$
• Geometry of A_g and Its Compactifications
• The Kodaira dimension of the moduli space of Prym varieties
• Rational maps between moduli spaces of curves and Gieseker-Petri divisors

Cited by in corpus (3)

• Extremal higher codimension cycles on moduli spaces of curves
• Koszul cohomology and applications to moduli
• Effective divisors on moduli spaces of curves and abelian varieties