Birational aspects of the geometry of M_g

Details Birational aspects of the geometry of M_g Birational aspects of the geometry of M_g

2008-10-03

arxiv.org/abs/0810.0702v2

Surveys in Differential Geometry Vol 14 (2010), 57-111

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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