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 \(M_2, \mkern 1.5mu\overline{\mkern1.5muM_2\mkern1.5mu}\mkern 1.5mu\). 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.