Espaces d'arcs et invariants d'Alexander

Guibert, Gil

doi:10.1007/pl00012442

Cited by 39 publications

(66 citation statements)

References 14 publications

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“…[5,6,10]) in the way stated in [9]. When f is the set of coordinate functions on the affine space A p k , our result is equivalent to a result obtained by Guibert in [8]. This paper is a natural continuation of [9], from which part of the notation and several results are borrowed.…”

Section: Introductionmentioning

confidence: 73%

Untitled

Guibert¹,

Loeser²,

Merle³

2005

Internat. Math. Res. Notices

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Section: Introductionmentioning

confidence: 73%

Untitled

Guibert¹,

Loeser²,

Merle³

2005

Internat. Math. Res. Notices

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“…Let us finally mention that our formula is sufficiently general to recover a combinatorial expression of Z f (T ) obtained by Guibert in [Gui02] when f is a polynomial that is nondegenerate with respect to its Newton polyhedron.…”

Section: 3])mentioning

confidence: 85%

“…As an application, we can recover a formula for Z f given by Guibert in [Gui02] when f is a polynomial that is nondegenerate with respect to its Newton polyhedron.…”

Section: A Formula For the Volume Poincaré Seriesmentioning

confidence: 99%

Computing zeta functions on log smooth models

Bultot

2015

Comptes Rendus. Mathématique

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We establish a formula for the volume Poincaré series of a log smooth scheme. This yields in particular a new expression and a smaller set of candidate poles for the motivic zeta function of a hypersurface singularity and of a degeneration of Calabi-Yau varieties. RésuméCalcul de fonctions zêta à partir de modèles log lisses. Nous établissons une formule pour la série volume de Poincaré d'un schéma log lisse. Ceci nous fournit en particulier une nouvelle expression et un ensemble réduit de candidats pôles pour la fonction zêta motivique d'une singularité d'hypersurface et d'une dégénération de variétés de Calabi-Yau.

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“…In this article we investigate the case of polynomials in k[x, y] in full generality (namely without any assumptions of convenience or non degeneracy w.r.t any Newton polygon) using ideas of Guibert in [16], Guibert, Loeser and Merle in [17], and the works of the first author and Veys in the case of an ideal of k[[x, y]] in [8,9] (see also [7] for the equivariant case). -Let E be a nonempty finite subset of N 2 .…”

Section: Introductionmentioning

confidence: 99%

Newton Transformations and the Motivic Milnor Fiber of a Plane Curve

Cassou-Noguès¹,

Raibaut²

2018

Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

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In this article we give an expression of the motivic Milnor fiber at infinity and the motivic nearby cycles at infinity of a polynomial f in two variables with coefficients in an algebraic closed field of characteristic zero. This expression is given in terms of some motives associated to the faces of the Newton polygons appearing in the Newton algorithm at infinity of f without any condition of convenience or non degeneracy. In the complex setting, we compute the Euler characteristic of the generic fiber of f in terms of the area of the surfaces associated to faces of the Newton polygons. Furthermore, if f has isolated singularities, we compute similarly the classical invariants at infinity λc(f ) which measures the non equisingularity at infinity of the fibers of f in P 2 , and we prove the equality between the topological and the motivic bifurcation sets and give an algorithm to compute them.

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Espaces d'arcs et invariants d'Alexander

Cited by 39 publications

References 14 publications

Untitled

Untitled

Computing zeta functions on log smooth models

Newton Transformations and the Motivic Milnor Fiber of a Plane Curve

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