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arXiv · 0810.0702

Birational aspects of the geometry of M_g

Gavril Farkas
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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.

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Gavril Farkas. 2009-08-10. Birational aspects of the geometry of M_g. https://arxiv.org/abs/0810.0702

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