The geometry of the moduli space of odd spin curves

Abstract

We describe the birational geometry of the moduli space S_g^{-} of odd spin curves (theta-characteristics) for all genera g. The odd spin moduli space is a uniruled variety for g<12, and of general type for g at least 12. Furthermore, for g<9 we use the existence of Mukai models of the moduli space of curves, to prove that S_g^{-} is unirational. Our results show that in genus 8, the odd spin moduli space in unirational, whereas its even counterpart is of Calabi-Yau type.

34 pages

References in corpus (4)

• Scorza quartics of trigonal spin curves and their varieties of power sums
• The intermediate type of certain moduli spaces of curves
• A Conversation with Murray Rosenblatt
• Effective divisors on \bar{M}_g, curves on K3 surfaces and the Slope Conjecture

Cited by in corpus (8)

• Effective divisors on moduli spaces of curves and abelian varieties
• Uniruledness of some moduli spaces of stable pointed curves
• The intermediate type of certain moduli spaces of curves
• Non-varying sums of Lyapunov exponents of Abelian differentials in low genus
• Moduli of theta-characteristics via Nikulin surfaces
• Theta characteristics and their moduli
• On the class of caustic on the moduli space of odd spin curves
• Tau function and moduli of spin curves