On extensions of the Torelli map

Abstract

The divisors on $\overline{\operatorname {M}}_g$ that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of $\operatorname{A}_g$ form a 2-dimensional extremal face of the nef cone of $\overline{\operatorname {M}}_g$, which is explicitly described.