The geometry of the moduli space of odd spin curves

Details The geometry of the moduli space of odd spin curves The geometry of the moduli space of odd spin curves

2010-04-02

arxiv.org/abs/1004.0278v1

Mathematics

Algebraic Geometry

31 pages

Scientific paper

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.

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