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Motivic-type invariants of blow-analytic equivalence

Satoshi Koike, Adam Parusiński (2003)

Annales de l'Institut Fourier

To a given analytic function germ f : ( ℝ d , 0 ) → ( ℝ , 0 ) , we associate zeta functions Z f , + , Z f , - ∈ ℤ [ [ T ] ] , defined analogously to the motivic zeta functions of Denef and Loeser. We show that our zeta functions are rational and that they are invariants of the blow-analytic equivalence in the sense of Kuo. Then we use them together with the Fukui invariant to classify the blow-analytic equivalence classes of Brieskorn polynomials of two variables. Except special series of singularities our method classifies as well the blow-analytic...

Nakamaye’s theorem on log canonical pairs

Salvatore Cacciola, Angelo Felice Lopez (2014)

Annales de l’institut Fourier

We generalize Nakamaye’s description, via intersection theory, of the augmented base locus of a big and nef divisor on a normal pair with log-canonical singularities or, more generally, on a normal variety with non-lc locus of dimension ≤ 1 . We also generalize Ein-Lazarsfeld-Mustaţă-Nakamaye-Popa’s description, in terms of valuations, of the subvarieties of the restricted base locus of a big divisor on a normal pair with klt singularities.

Nœuds algébriques

Lê Dũng Tráng (1973)

Annales de l'institut Fourier

Nous donnons un résumé des principaux résultats récents obtenus sur les nœuds algébriques.

Number of singular points of an annulus in ℂ 2

Maciej Borodzik, Henryk Zołądek (2011)

Annales de l’institut Fourier

Using BMY inequality and a Milnor number bound we prove that any algebraic annulus ℂ * in ℂ 2 with no self-intersections can have at most three cuspidal singularities.

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