Linear sections of the Severi variety and moduli of curves

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 ${\bar{M}}_g$. We use this to derive lower bounds for the slopes of effective divisors on ${\bar{M}}_g$. Another application of our results is to various enumerative problems on $V_{d,g}$.

28 pages, 4 figures

Cited by in corpus (2)

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