Recursive algorithm and log-concavity of representations on the cohomology of \mathcal M_0,n

2024/08/20 by Jinwon Choi, Choi, Jinwon, Young‐Hoon Kiem +3
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2408.10728

openalex publication_date 2024/08/20 · openalex created_date 2024/10/01 · openalex updated_date 2026/07/28

Abstract

We provide a programmable recursive algorithm for the \mathbbS_n-representations on the cohomology of the moduli spaces \mathcal M_0,n of n-pointed stable curves of genus 0. As an application, we find explicit inductive and asymptotic formulas for the invariant part H^*(\mathcal M_0,n/\mathbbS_n) and prove that its Poincaré polynomial is asymptotically log-concave. Based on numerical computations with our algorithm, we further conjecture that the sequence \H^2k(\mathcal M_0,n)\ of \mathbbS_n-modules is equivariantly log-concave.

Related

• Representations on the cohomology of M_0,n
• Characteristic polynomial of M_0,n and log-concavity
• On the cohomology of moduli spaces of (weighted) stable rational curves
• Improved Bounds on Ultra-Log Concavity of the Grothendieck Class of M_0,n
• The action of S_n on the cohomology of M_0,n(R)