The Chow rings of $M_7$, $M_8$, and $M_9$

Abstract: The rational Chow ring of the moduli space of smooth curves is known when the genus is at most $6$ by work of Mumford ($g=2$), Faber ($g=3$, $4$), Izadi ($g=5$), and Penev-Vakil ($g=6$). In each case, it is generated by the tautological classes. On the other hand, van Zelm has shown that the bielliptic locus is not tautological when $g=12$. In recent joint work with Hannah Larson, we show that the Chow rings of $M_7$, $M_8$, and $M_9$ are generated by tautological classes, which determines the Chow ring by work of Faber. I will explain an overview of the proof with an emphasis on the special geometry of curves of low genus and low gonality.

algebraic geometry

Audience: researchers in the topic

( slides | video )

Comments: The synchronous discussion for Sam Canning’s talk is taking place not in zoom-chat, but at tinyurl.com/2021-04-16-sc (and will be deleted after ~3-7 days).

---

Stanford algebraic geometry seminar

Series comments: The seminar was online for a significant period of time, but for now is solely in person. More seminar information (including slides and videos, when available): agstanford.com

---