
## 4. Rational subvarieties of the moduli space of rational curves and of abelian varieties

1. #### Problem 4.1.

When is $\mathcal{M}_{g,n}$, $\mathcal{A}_{g}[d]$ or $\mathcal{K3}_{d}$ unirational over char. $p$? When is $\mathcal{M}_{1,n}$ unirational for $n\geq 11$?
• #### Problem 4.2.

Find rational curves in $\mathcal{A}_{g}$ in char. $p$, that do not lift to char. $0$.
• #### Problem 4.3.

What are the rationality properties of $\mathcal{A}_{g,s.s.}$? You can ask the same question for Newton polygon strata.
• #### Problem 4.4.

Are complete rational curves in $\mathcal{A}_{g}$ dense in char. $p$?

Cite this as: AimPL: Rational subvarieties in positive characteristic, available at http://aimpl.org/ratsubvarpos.