Limits of log canonical thresholds
| dc.creator | de Fernex, Tommaso | |
| dc.creator | Mustata, Mircea | |
| dc.date | 2007-10-26 | |
| dc.date | 2009-02-02 | |
| dc.date.accessioned | 2026-07-07T12:35:54Z | |
| dc.date.available | 2026-07-07T12:35:54Z | |
| dc.description | Let T_n denote the set of log canonical thresholds of pairs (X,Y), with X a nonsingular variety of dimension n, and Y a nonempty closed subscheme of X. Using non-standard methods, we show that every limit of a decreasing sequence in T_n lies in T_{n-1}, proving in this setting a conjecture of Kollár. We also show that T_n is a closed subset in the set of real numbers; in particular, every limit of log canonical thresholds on smooth varieties of fixed dimension is a rational number. As a consequence of this property, we see that in order to check Shokurov's ACC Conjecture for all T_n, it is enough to show that 1 is not a point of accumulation from below of any T_n. In a different direction, we interpret the ACC Conjecture as a semi-continuity property for log canonical thresholds of formal power series. | |
| dc.description | 26 pages; revised version, to appear in Ann. Sci. Ecole Norm. Sup | |
| dc.identifier | https://arxiv.org/abs/0710.4978 | |
| dc.identifier | http://arxiv.org/abs/0710.4978 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/217917 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14B05 (Primary); 03H05, 14E30 (Secondary) | |
| dc.title | Limits of log canonical thresholds | |
| dc.type | text |