Multiscale differentials and wonderful models

2025/04/15 by Prabhat Devkota, Devkota, Prabhat, Antonios-Alexandros Robotis +3 · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.2504.11534

Abstract

We study the relationships between several varieties parametrizing marked curves with differentials in the literature. More precisely, we prove that the space B_n of multiscale differentials of genus 0 with n+1 marked points of orders (0,…,0,-2) is a wonderful variety. This shows that the Chow ring of B_n is generated by the classes of a collection of smooth boundary divisors with normal crossings subject to simple and explicit linear and quadratic relations. Furthermore, we realize B_n as a subvariety of the space A_n of multiscale lines and prove that B_n can be realized as the normalized Chow quotient of A_n by a natural ℂ^*-action.

Citations

• The space of augmented stability conditions
• Logarithmic tautological rings of the moduli spaces of curves
• Cohomology of Moduli Space of Multiscale Differentials in Genus 0
• Small resolutions of moduli spaces of scaled curves
• Marked nodal curves with vector fields
• The Chern classes and the Euler characteristic of the moduli spaces of abelian differentials
• A semi-small decomposition of the Chow ring of a matroid
• The moduli space of multi-scale differentials
• Teichmüller dynamics in the eyes of an algebraic geometer
• Wonderful compactification of an arrangement of subvarieties
• Chow rings of toric varieties defined by atomic lattices
• Stability conditions on triangulated categories
• Moduli spaces of weighted pointed stable curves
• Polydiagonal compactification of configuration spaces
• Rational Curves on Algebraic Varieties
• Wonderful models of subspace arrangements
• Chow quotients of Grassmannian I
• Geometry of Algebraic Curves
• The irreducibility of the space of curves of given genus

Cited by

• The \mathbbS_n-equivariant Chow polynomial of the braid matroid

Related

• Cohomology of Moduli Space of Multiscale Differentials in Genus 0
• A tale of two moduli spaces: logarithmic and multi-scale differentials
• The moduli space of multi-scale differentials
• Gorenstein contractions of multiscale differentials
• Rationality and Chow-Kuenneth decompositions for some moduli stacks of curves