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arXiv:1011.3699 [math.AG]AbstractReferencesReviewsResources

Valuations and asymptotic invariants for sequences of ideals

Mattias Jonsson, Mircea Mustata

Published 2010-11-16, updated 2011-10-20Version 3

We study asymptotic jumping numbers for graded sequences of ideals, and show that every such invariant is computed by a suitable real valuation of the function field. We conjecture that every valuation that computes an asymptotic jumping number is necessarily quasi-monomial. This conjecture holds in dimension two. In general, we reduce it to the case of affine space and to graded sequences of valuation ideals. Along the way, we study the structure of a suitable valuation space.

Comments: 49 pages; v2: we now work more generally in the setting of arbitrary excellent regular schemes; some details regarding the definition of quasi-monomial valuations have been added in Section 3.1; v3: minor changes, this is the final version, to appear in Ann. Inst. Fourier (Grenoble)
Categories: math.AG, math.AC
Subjects: 14F18, 12J20, 14B05
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