The intermediate type of certain moduli spaces of curves
Algebraic Geometry
2009-11-02 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0910.3905,
title = {The intermediate type of certain moduli spaces of curves},
author = {Gavril Farkas and Alessandro Verra},
journal= {arXiv preprint arXiv:0910.3905},
year = {2009}
}
Comments
20 pages. Stronger results in Section 5, concerning the birational type of M_{g, n} for genus at most 8