The birational type of the moduli space of even spin curves

Abstract

We determine the Kodaira dimension of the moduli space of even spin curves for all genera, with one possible exception: The scheme S_g has negative Kodaira dimension for g<8 and it is of general type for g>8. The Kodaira dimension of S_8 is non-negative.

arXiv comment9 pages. Improved presentation, to appear in Advances in Mathematics

References in corpus (2)

• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• The moduli space of genus 4 even spin curves is rational