# Geometry and Arithmetic

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#### DOI: 10.4171/119-1/8

On extensions of the Torelli map

Angela Gibney[1]

(1) University of Georgia, Athens, USA

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.

Keywords: Torelli map, nef cone, moduli space of curves