Birational aspects of the geometry of M_g
Algebraic Geometry
2010-12-23 v2
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.
Keywords
Cite
@article{arxiv.0810.0702,
title = {Birational aspects of the geometry of M_g},
author = {Gavril Farkas},
journal= {arXiv preprint arXiv:0810.0702},
year = {2010}
}
Comments
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