Valuations and asymptotic invariants for sequences of ideals

Details Valuations and asymptotic invariants for sequences of ideals Valuations and asymptotic invariants for sequences of ideals

2010-11-16

arxiv.org/abs/1011.3699v3

Mathematics

Algebraic Geometry

49 pages; v2: we now work more generally in the setting of arbitrary excellent regular schemes; some details regarding the def

Scientific paper

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.

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