Algebraic intersection for hyperbolic surfaces

2024/04/24 by Manman Jiang, Jiang, Manman, Huiping Pan +1
Computer Science · Engineering · Mathematics · #30F45 #30F60 #32G15 #Advanced Numerical Analysis Techniques #Complex Variables (math.CV) #Computational Geometry and Mesh Generation #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2404.15921

openalex publication_date 2024/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the algebraic intersection form of hyperbolic surfaces of genus g has a minimum in the moduli space and that the minimum grows in the order (log g)^-2 in terms of the genus. We also describe the asymptotic behavior of the algebraic intersection form in the moduli space as the homologically systolic length goes to zero.

Related

• Intersection Number, Length, and Systole on Compact Hyperbolic Surfaces
• The asymptotic Weil-Petersson form and intersection theory on M_g,n
• Determining surfaces by short curves and applications
• The homology systole of hyperbolic Riemann surfaces
• Limit points of the branch locus of M_g