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

2025/11/03 by Choi, Daebeom
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · doi:10.48550/arxiv.2511.02019

Abstract

We develop a new method for establishing the extremality in the closed cone of effective curves on the moduli space of curves and determine the extremality of many boundary 1-strata. As a consequence, by using a general criterion for non-semiampleness which extends Keel's argument, we demonstrate that a substantial portion of the cone of nef divisors of M_g,n is not semiample. As an application, we construct the first explicit example of a non-contractible extremal ray of the closed cone of effective curves on M_3,n. Our method relies on two main ingredients: (1) the construction of a new collection of nef divisors on M_g,n, and (2) the identification of a tractable inductive structure on the Picard group, arising from Knudsen's construction of M_g,n.

Citations

• Symmetric and non-symmetric F-conjectures are equivalent
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• Complete Subvarieties of \rmM_g,n and a Lifting Problem
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• On the cone of effective 2-cycles on M_0,7
• The cone of type A, level one conformal blocks divisors
• On extensions of the Torelli map
• Chern classes of conformal blocks
• Divisors in the moduli spaces of curves
• Moduli spaces of weighted pointed stable curves
• Oort's conjecture for A_g
• The Q-Picard group of the moduli space of curves in positive characteristic
• Towards the ample cone of \mgn
• Chow quotients of Grassmannian I

Related

• Contractible Extremal Rays on M_0,n
• Extremality of Rational Tails Boundary Strata in M_g,n
• Extremal effective divisors of Brill-Noether and Gieseker-Petri type in \mathcal M_1,n
• Extremal divisors on moduli spaces of rational curves with marked points
• On the effective cone of M_g,n