A note on Hilbert schemes of nodal curves

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dc.creatorRan, Ziv
dc.date2004-10-03
dc.date.accessioned2026-07-07T05:12:48Z
dc.date.available2026-07-07T05:12:48Z
dc.descriptionWe study completely the Hilbert scheme and punctual Hilbert scheme of a nodal curve, and the relative Hilbert scheme of a family of curves acquiring a node. The results are then extended, less completely, to flag Hilbert schemes, parametrizing chains of subschemes. We find, notably, that if the total space $X$ of a family $X/B$ is smooth (over an algebraically closed field $\k$), then the relative Hilbert scheme $Hilb_m(X/B)$ is smooth over $\k$ and the flag Hilbert schemes are normal and locally complete intersection, but generally singular.
dc.description16 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0410037
dc.identifierhttp://arxiv.org/abs/math/0410037
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/72715
dc.subjectAlgebraic Geometry
dc.subject14C05
dc.titleA note on Hilbert schemes of nodal curves
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