GIT stability of weighted pointed curves
| dc.creator | Swinarski, David | |
| dc.date | 2008-01-08 | |
| dc.date.accessioned | 2026-07-07T08:53:19Z | |
| dc.date.available | 2026-07-07T08:53:19Z | |
| dc.description | Here 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.description | 41 pages | |
| dc.identifier | https://arxiv.org/abs/0801.1288 | |
| dc.identifier | http://arxiv.org/abs/0801.1288 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145578 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14L24; 14H10 | |
| dc.title | GIT stability of weighted pointed curves | |
| dc.type | text |