Sequences of LCT-polytopes
Algebraic Geometry
2011-05-04 v3
Abstract
To r ideals on a germ of smooth variety X one attaches a rational polytope in the r-dimensional Euclidean space (the LCT-polytope) that generalizes the notion of log canonical threshold in the case of one ideal. We study these polytopes, and prove a strong form of the Ascending Chain Condition in this setting: we show that if a sequence P_m of such LCT-polytopes converges to a compact subset Q in the Hausdorff metric, then Q is equal to the intersection of all but finitely many of the P_m. Furthermore, Q is an LCT-polytope.
Keywords
Cite
@article{arxiv.1002.4163,
title = {Sequences of LCT-polytopes},
author = {Anatoly Libgober and Mircea Mustata},
journal= {arXiv preprint arXiv:1002.4163},
year = {2011}
}
Comments
16 pages; v3: minor corrections, to appear in Mathematical Research Letters