Algebra, Geometry, & Number Theory Seminar

Strata of differentials are natural subvarieties of moduli spaces of pointed curves M_{g,n}, defined by the condition that the sum of marked points with some chosen multiplicity are a (pluri)canonical divisor. The tautological ring of strata of differentials is the subring of their Chow ring generated by the restrictions of tautological classes on M_{g,n}. Earlier work of D. Chen explains some relations among the restrictions of tautological classes and shows that the tautological ring of strata of differentials is generated by divisor classes. In recent joint work with D. Chen, we prove that these are the only relations in degrees that are small compared to the genus and number of simple zeros. Moreover, for strata of holomorphic differentials, we prove that, when the simple zeros are unordered, all cohomology classes are tautological in degrees that are small compared to the genus and number of simple zeros.