Asymptotic invariants of base loci

Details Asymptotic invariants of base loci Asymptotic invariants of base loci

2003-08-12

arxiv.org/abs/math/0308116v2

Mathematics

Algebraic Geometry

26 pages, 1 figure; shorter version with more efficient exposition and more general version of asymptotic invariants; notation

Scientific paper

The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. We distinguish an open dense subset of the real big cone, called the stable locus, consisting of the set of classes on which the asymptotic base locus is locally constant. The asymptotic invariants define continuous functions on the big cone, whose vanishing characterizes, roughly speaking, the unstable locus. We show that for toric varieties at least, there exists a polyhedral decomposition of the big cone on which these functions are polynomial.

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