Richard Haburcak
The Ohio State University
Title
Non-tautological Cycles on Moduli Spaces of Smooth Curves
Abstract
The moduli space of algebraic curves is a central object of study, and its cohomology ring is deeply related to spaces of modular forms. The tautological ring is a subring of the cohomology of the moduli space of stable curves which contains most cohomology classes of geometric interest and is simpler to study. A question of interest is therefore how different the tautological ring is from the full cohomology. The first known example of a non-tautological algebraic class was discovered by Graber and Pandharipande, which was significantly generalized by van Zelm to find an infinite family of non-tautological classes. On the other hand, very little is known about non-tautological classes on the moduli space of smooth curves. In joint work with Arena, Canning, Clader, Li, Mok, and Tamborini, we show that there are non-tautological classes on the moduli space of smooth marked curves for an infinite family of genera.
