Linear sections of the Severi variety and moduli of curves

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dc.creatorFedorchuk, Maksym
dc.date2007-10-08
dc.date.accessioned2026-07-07T08:34:48Z
dc.date.available2026-07-07T08:34:48Z
dc.descriptionWe 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 $V_{d,g}$.
dc.description28 pages, 4 figures
dc.identifierhttps://arxiv.org/abs/0710.1623
dc.identifierhttp://arxiv.org/abs/0710.1623
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/139565
dc.subjectAlgebraic Geometry
dc.subject14H10, 14H50, 14N10
dc.titleLinear sections of the Severi variety and moduli of curves
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