A Hurwitz divisor on the Moduli of Prym curves

2021/04/30 by Bud, Viorel Andrei, Bud, Andrei
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics

paper · doi:10.48550/arxiv.2104.14947

openalex publication_date 2021/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/04/28

Abstract

For genus g=2i≥4 and the length g-1 partition μ = (4,2,…,2,-2,…,-2) of 0, we compute the first coefficients of the class of D(μ) in Pic_ℚ(R_g), where D(μ) is the divisor consisting of pairs [C,η]∈ R_g with η ≅ O_C(2x₁+x₂+⋯ + x_i-1-x_i-⋯-x_2i-1) for some points x₁,…, x_2i-1 on C. We further provide several enumerative results that will be used for this computation.

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• Divisors on Hurwitz spaces: an appendix to 'The cycle classes of divisorial Maroni loci'
• The class of the Prym-Brill-Noether divisor
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