Valuations and asymptotic invariants for sequences of ideals

Mattias Jonsson[1]; Mircea Mustaţă[1]

  • [1] Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 6, page 2145-2209
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Jonsson, Mattias, and Mustaţă, Mircea. "Valuations and asymptotic invariants for sequences of ideals." Annales de l’institut Fourier 62.6 (2012): 2145-2209. <http://eudml.org/doc/251034>.

@article{Jonsson2012,
abstract = {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.},
affiliation = {Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA; Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA},
author = {Jonsson, Mattias, Mustaţă, Mircea},
journal = {Annales de l’institut Fourier},
keywords = {Graded sequence of ideals; multiplier ideals; log canonical threshold; valuation; graded sequence of ideals},
language = {eng},
number = {6},
pages = {2145-2209},
publisher = {Association des Annales de l’institut Fourier},
title = {Valuations and asymptotic invariants for sequences of ideals},
url = {http://eudml.org/doc/251034},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Jonsson, Mattias
AU - Mustaţă, Mircea
TI - Valuations and asymptotic invariants for sequences of ideals
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 6
SP - 2145
EP - 2209
AB - 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.
LA - eng
KW - Graded sequence of ideals; multiplier ideals; log canonical threshold; valuation; graded sequence of ideals
UR - http://eudml.org/doc/251034
ER -

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