On extensions of the Torelli map

2011/04/19 by Angela Gibney, Gibney, Angela · 2 citations
Mathematics · #14E30 #14H10 #14K10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algorithm #Combinatorics #Compactification (mathematics) #Computer science #Cone (formal languages) #Extension (predicate logic) #FOS: Mathematics #Face (sociological concept) #Geometry #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Linguistics #Mathematics #Philosophy #Physics #Pure mathematics #Toroid #math.AG #msc:14E30 #msc:14H10 #msc:14K10

paper · pdf · doi:10.48550/arxiv.1104.3788

published in arXiv (Cornell University) (Cornell University) · 10 pages, 1 figure

arxiv created 2011/04/19 · openalex publication_date 2011/04/19 · arxiv updated 2015/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The divisors on M_g that arise as the pullbacks of ample divisors along any extension of the Torelli map to any toroidal compactification of A_g form a 2-dimensional extremal face of the nef cone of M_g, which is explicitly described.

Citations

• Conformal blocks divisors on M_0,n from sl₂
• Log minimal model program for the moduli space of stable curves: The first flip
• Voronoi-Dickson Hypothesis on Perfect Forms and L-types

Cited by

• Extremal effective curves and non-semiample line bundles on \rmM_g,n

Related

• Self-intersection of the Torelli map
• Nef divisors on M_0,n from GIT
• The nef cone of toroidal compactifications of \cal A₄
• Nef Divisors on Moduli Spaces of Abelian Varieties
• The Prym map on divisors, and the slope of A₅