On extensions of the Torelli map
Angela Gibney

TL;DR
This paper characterizes the divisors on the moduli space of curves that come from extensions of the Torelli map to toroidal compactifications, revealing a specific extremal face of the nef cone.
Contribution
It explicitly describes the 2-dimensional extremal face of the nef cone of ar{M}_g associated with these divisors, extending understanding of the Torelli map's geometric properties.
Findings
Identifies a 2-dimensional extremal face of the nef cone of ar{M}_g.
Describes the divisors arising from extensions of the Torelli map.
Provides an explicit description of this extremal face.
Abstract
The divisors on that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of form a 2-dimensional extremal face of the nef cone of , which is explicitly described.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology
