Sharp slope bounds for sweeping families of trigonal curves

2012/11/12 by Anand Deopurkar, Deopurkar, Anand, Anand Patel +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1211.2827

openalex publication_date 2012/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish sharp bounds for the slopes of curves in M_g that sweep the locus of trigonal curves, proving Stankova-Frenkel's conjectured bound of 7+6/g for even g and obtaining the bound 7+20/(3g+1) for odd g. For even g, we find an explicit expression of the so-called Maroni divisor in the Picard group of the space of admissible triple covers. For odd g, we describe the analogous extremal effective divisor and give a similar explicit expression.

Citations

• Moduli of Trigonal Curves

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