Linear Sections of the Severi Variety and Moduli of Curves
نویسنده
چکیده
We study the Severi variety Vd,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 Mg. We use this to derive lower bounds for the slopes of effective divisors on Mg . Another application of our results is to various enumerative problems on Vd,g.
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