# 2021-04-16

## Stanford AG: Samir Canning, joint with Hannah Larson

• What is the universal curve over $$M_g$$? #todo/questions

• What is the tautological ring, and how does it relate to the Chow ring? #todo/questions

• What are the kappa classes? #todo/questions

• Question: when does $$A^*(M_g) = R^*(M_g)$$?

• The integral Chow ring is very unknown. We know it only very recently for $$M_2, \mkern 1.5mu\overline{\mkern-1.5muM_2\mkern-1.5mu}\mkern 1.5mu$$. Compare to rational Chow rings: we know them as quotients of polynomial rings for $$M_g, g\leq 23$$.

• Can stratify $$M_g$$ by gonality.

• What are hyperelliptic curves?

I definitely have known this at several points in time, yeesh.

• Look at Hurwitz space : moduli space of degree $$n$$ covers of $${\mathbf{P}}^1$$ by smooth genus $$g$$ curves? At least this specific one is.