Integral Chow rings of modular compactifications of M_{1,n≤ 6}

2025/05/07 by Luca Battistella, Battistella, Luca, Andrea Di Lorenzo +1
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2505.04587

Abstract

For n≤ 6, we compute the integral Chow ring of every modular compactification of M_1,n parametrising only Gorenstein curves with smooth, distinct markings. These include the Deligne--Mumford, Schubert, and Smyth compactifications, and many more. They can all be excised from the stack of log-canonically polarised Gorenstein curves. The Chow ring of the latter admits a simple, combinatorial description, which we compute by patching along a natural stratification by core level. We further deduce that all these modular compactifications satisfy the Chow-Künneth generation property, that the cycle class map is an isomorphism, and for n=4 we study whether the Getzler's relation hold integrally.

Citations

• On the Chow and cohomology rings of moduli spaces of stable curves
• Moduli of genus one curves with two marked points as a weighted blow-up
• Polarized twisted conics and moduli of stable curves of genus two
• Chow rings of stacks of prestable curves II
• Fano manifolds of index n-2 and the cone conjecture
• Modular Compactifications of M_1,n II
• Towards a classification of modular compactifications of the moduli space of curves
• A geometric construction of Getzler's relation
• Equivariant intersection theory

Related

• Wall-crossing integral Chow rings of \mathcal M_1,n
• A modular compactification of \M_1,n from\n A_\∞-structures
• The integral Chow ring of M_1,n for n=3,…,10
• Modular compactifications of M_1,n
• On compactifications of M_g,n with colliding markings