We study Quot schemes of rank 0 quotients on smooth projective curves. These Quot schemes exhibit a rich and highly structured geometry, with formal parallels to the Hilbert schemes of points on surfaces.

In this talk, we first note formulas for the twisted \chi_y-genera with values in tautological line bundles pulled back from the symmetric product via the Quot-to-Chow morphism, and for the associated twisted Hodge numbers. Going further, we give formulas for the level 2 (twisted) elliptic genus for quotients of a vector bundle of even rank. We also discuss the case of level \ell elliptic genera, for higher values of \ell.