The intermediate type of certain moduli spaces of curves

Details The intermediate type of certain moduli spaces of curves The intermediate type of certain moduli spaces of curves

2009-10-20

arxiv.org/abs/0910.3905v2

Mathematics

Algebraic Geometry

20 pages. Stronger results in Section 5, concerning the birational type of M_{g, n} for genus at most 8

Scientific paper

A well-known principle of Mumford asserts that all moduli spaces of curves are varieties of general type, except a finite number of cases that occur for relatively small genus, when these varieties tend to be uniruled. In all known cases, the transition from uniruledness to being of general type is quite sudden. For the first time, we show that naturally defined moduli spaces of curves can have intermediate birational type. We show that the moduli space of even spin curves of genus 8 is of Calabi-Yau type. Then we prove that the 41-dimensional moduli space M_{11, 11} of 11-pointed curves of genus 11, has Kodaira dimension 19.

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