Sequences of LCT-polytopes

Details Sequences of LCT-polytopes Sequences of LCT-polytopes

2010-02-22

arxiv.org/abs/1002.4163v3

Mathematics

Algebraic Geometry

16 pages; v3: minor corrections, to appear in Mathematical Research Letters

Scientific paper

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.

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