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[unknown]

Todor Milanov, Yefeng Shen (0)

Annales de l’institut Fourier

[unknown]

Alessandro Ardizzoni, Federica Galluzzi, Francesco Vaccarino (0)

Annales de l’institut Fourier

Valuations and asymptotic invariants for sequences of ideals

Mattias Jonsson, Mircea Mustaţă (2012)

Annales de l’institut Fourier

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.

Weakly-exceptional quotient singularities

Dmitrijs Sakovics (2012)

Open Mathematics

A singularity is said to be weakly-exceptional if it has a unique purely log terminal blow-up. In dimension 2, V. Shokurov proved that weakly-exceptional quotient singularities are exactly those of types D n, E 6, E 7, E 8. This paper classifies the weakly-exceptional quotient singularities in dimensions 3 and 4.

Zeta functions and blow-Nash equivalence

Goulwen Fichou (2005)

Annales Polonici Mathematici

We propose a refinement of the notion of blow-Nash equivalence between Nash function germs, which has been introduced in [2] as an analog in the Nash setting of the blow-analytic equivalence defined by T.-C. Kuo [13]. The new definition is more natural and geometric. Moreover, this equivalence relation still does not admit moduli for a Nash family of isolated singularities. But though the zeta functions constructed in [2] are no longer invariants for this new relation, thanks to a Denef & Loeser...

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