2021/05/24 by Dawei Chen, Chen, Dawei
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #math.AG #math.DS #math.GT
paper · pdf · doi:10.48550/arxiv.2105.11487
arxiv created 2021/05/24 · openalex publication_date 2021/05/24 · arxiv updated 2021/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The flex locus parameterizes plane cubics with three collinear cocritical points under a projection, and the gothic locus arises from quadratic differentials with zeros at a fiber of the projection and with poles at the cocritical points. The flex and gothic loci provide the first example of a primitive, totally geodesic subvariety of moduli space and new \rm SL2(ℝ)-invariant varieties in Teichmüller dynamics, as discovered by McMullen-Mukamel-Wright. In this paper we determine the divisor class of the flex locus as well as various tautological intersection numbers on the gothic locus. For the case of the gothic locus our result confirms numerically a conjecture of Chen-Möller-Sauvaget about computing sums of Lyapunov exponents for \rm SL2(ℝ)-invariant varieties via intersection theory.