GIT stability of weighted pointed curves

dc.creatorSwinarski, David
dc.date2008-01-08
dc.date.accessioned2026-07-07T08:53:19Z
dc.date.available2026-07-07T08:53:19Z
dc.descriptionHere I give a direct proof that smooth curves with distinct marked points are asymptotically Hilbert stable with respect to a wide range of parameter spaces and linearizations. This result can be used to construct the coarse moduli space of Deligne-Mumford stable pointed curves \bar M_g,n and Hassett's moduli spaces of weighted pointed curves \bar M_g,A (though the full construction of the moduli spaces is not contained in this paper, only the stability proof). My proof follows Gieseker's approach to reduce to the GIT problem to a combinatorial problem, though the solution is very different. The action of any 1-PS lambda on a curve C in P^N gives rise to weighted filtrations of H^0 (C, O(1)) and H^0 (C, O(m)), and I give a recipe in terms of the combinatorics of the base loci of the stages of these filtrations for showing that C is stable with respect to lambda.
dc.description41 pages
dc.identifierhttps://arxiv.org/abs/0801.1288
dc.identifierhttp://arxiv.org/abs/0801.1288
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/145578
dc.subjectAlgebraic Geometry
dc.subject14L24; 14H10
dc.titleGIT stability of weighted pointed curves
dc.typetext

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