Linear sections of the Severi variety and moduli of curves

2007/10/08 by Maksym Fedorchuk, Fedorchuk, Maksym
Mathematics · #14H10 #14H50 #14N10 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H10 #msc:14H50 #msc:14N10

paper · pdf · doi:10.48550/arxiv.0710.1623

28 pages, 4 figures

arxiv created 2007/10/08 · arxiv updated 2009/12/01

Abstract

We study the Severi variety V_d,g of plane curves of degree d and geometric genus g. Corresponding to every such variety, there is a one-parameter family of genus g stable curves whose numerical invariants we compute. Building on the work of Caporaso and Harris, we derive a recursive formula for the degrees of the Hodge bundle on the families in question. For d large enough, these families induce moving curves in M_g. We use this to derive lower bounds for the slopes of effective divisors on M_g. Another application of our results is to various enumerative problems on V_d,g.

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