|Location:||MSRI: Simons Auditorium|
Moduli spaces of spin curves parameterizing roots of canonical bundles
over curves of genus g, are interesting covers of the moduli space of
curves. For instance their enumerative geometry is highly non-trivial and
the generating function of intersection numbers of tautological classes
satisfies differential equations coming from integrable systems.
We discuss the birational and enumerative geometry of the spin moduli
space S_g and prove among other things that the even moduli space of genus
g spin curves is of general type for g>8, while its odd counterpart is of
general type for g>11. We also present evidence that S_8 is a
21-dimensional Calabi-Yau variety.