Limits of stable pairs
| dc.creator | Alexeev, Valery | |
| dc.date | 2006-07-26 | |
| dc.date | 2007-11-05 | |
| dc.date.accessioned | 2026-07-07T08:40:19Z | |
| dc.date.available | 2026-07-07T08:40:19Z | |
| dc.description | Let (X_0,B_0) be the canonical limit of a one-parameter family of stable pairs, provided by the log Minimal Model Program. We prove that X_0 is S2 and that [B_0] is S_1, as an application of a general local statement: if (X,B+εD) is log canonical and D is Q-Cartier then D is S2 and [B] \cap D is S1, i.e. has no embedded components. When B has coefficients smaller than 1, examples due to Hacking and Hassett show that B_0 may indeed have embedded primes. We resolve this problem by introducing a category of stable branchpairs. We prove that the corresponding moduli functor is proper for families with normal generic fiber. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0607684 | |
| dc.identifier | http://arxiv.org/abs/math/0607684 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141337 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Commutative Algebra | |
| dc.title | Limits of stable pairs | |
| dc.type | text |