Prym enumerative geometry and a Hurwitz divisor in R_2i

2022/01/28 by Bud, Andrei
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.12009

Abstract

For i≥2, we compute the first coefficients of the class [D(μ;3)] in the rational Picard group of the moduli of Prym curves R_2i, where D(μ;3) is the divisor parametrizing pairs [C,η] for which there exists a degree 2i map π\colon C→ ℙ¹ having ramification profile (2,…,2) above two points q₁, q₂, a triple ramification somewhere else and satisfying O_C(\fracπ^*(q₁)-π^*(q₂)2)≅ η. Furthermore, we provide several new Prym enumerative results related to this situation.

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