Isoresidual fibrations and the birational geometry of moduli of pointed stable curves

2025/10/29 by Mullane, Scott
#Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2510.25044

Abstract

We show that the pseudo-effective cone of divisors of M_0,n is not polyhedral for n≥ 8 by constructing an extremal non-polyhedral ray of the dual cone of moving curves via maps on meromorphic strata of differentials returning the residues at the poles of the parameterised differentials. An immediate corollary is that these spaces are not Mori Dream Spaces.

Citations

• Symmetric and non-symmetric F-conjectures are equivalent
• Connected components of generalized strata of meromorphic differentials with residue conditions
• Isoresidual curves
• Counting differentials with fixed residues
• Stratified braid groups: monodromy
• Blown-up toric surfaces with non-polyhedral effective cone
• Isoresidual fibration and resonance arrangements
• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials
• Non-polyhedral effective cones from the moduli space of curves
• The moduli space of multi-scale differentials
• Birational geometry of blow-ups of projective spaces along points and lines
• On blowing up the weighted projective plane
• Extremal divisors on moduli spaces of rational curves with marked points
• Isolation, equidistribution, and orbit closures for the SL(2,R) action\n on Moduli space
• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Pseudo-effective classes and pushforwards
• The cone of type A, level one conformal blocks divisors
• Square-tiled surfaces and rigid curves on moduli spaces
• Equations for Chow and Hilbert Quotients
• The pseudo-effective cone of a compact Kähler manifold and varieties of negative Kodaira dimension
• Moduli spaces of local systems and higher Teichmuller theory
• On the effective cone of the moduli space of pointed rational curves
• Towards the ample cone of \mgn
• Mori Dream Spaces and GIT

Related

• Non-polyhedral effective cones from the moduli space of curves
• Duality and polyhedrality of cones for Mori dream spaces
• Contractible Extremal Rays on M_0,n
• The Mori cones of moduli spaces of pointed curves of small genus
• Towards Mori's program for the moduli space of stable maps