Motivic Milnor fibers of a rational function

Michel Raibaut

doi:10.1016/j.crma.2012.04.021

Algebraic Geometry

Motivic Milnor fibers of a rational function

Presented by: Claire Voisin

Michel Raibaut ¹

¹ Institut de mathématiques de Jussieu, 4, place Jussieu, case 247, 75252 Paris cedex 5, France

Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 519-524.

Abstract
Résumé

Let P and Q be two complex polynomials and f be the induced rational function. In this Note we define a motivic Milnor fiber of the germ of f at an indeterminacy point x for a value a, a motivic Milnor fiber of f for a value a and finally motivic bifurcation sets.

Soit P et Q deux polynômes à coefficients complexes et f lʼapplication rationnelle quotient induite. Dans cette Note nous introduisons une fibre de Milnor motivique du germe de f en un point dʼindétermination x pour une valeur a, puis une fibre de Milnor motivique de f pour une valeur a et enfin des ensembles de bifurcation motiviques.

Received: 2012-02-15
Accepted: 2012-04-27
Published online: 2012-05-01

DOI: 10.1016/j.crma.2012.04.021

Author's affiliations:

Michel Raibaut ¹

¹ Institut de mathématiques de Jussieu, 4, place Jussieu, case 247, 75252 Paris cedex 5, France

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     title = {Motivic {Milnor} fibers of a rational function},
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Michel Raibaut. Motivic Milnor fibers of a rational function. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 519-524. doi : 10.1016/j.crma.2012.04.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.04.021/

References
Cited by

[1] Jan Denef; François Loeser Motivic Igusa zeta functions, J. Algebraic Geom., Volume 7 (1998) no. 3, pp. 505-537

[2] Jan Denef; François Loeser Geometry on arc spaces of algebraic varieties, Barcelona, 2000 (Progr. Math.), Volume vol. 201, Birkhäuser, Basel (2001), pp. 327-348

[3] Jan Denef; François Loeser Lefschetz numbers of iterates of the monodromy and truncated arcs, Topology, Volume 41 (2002) no. 5, pp. 1031-1040

[4] Gil Guibert; François Loeser; Michel Merle Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink, Duke Math. J., Volume 132 (2006) no. 3, pp. 409-457

[5] Sabir Gusein-Zade; Ignacio Luengo; Alejandro Melle Hernández Zeta functions of germs of meromorphic functions, and the Newton diagram, Funktsional. Anal. i Prilozhen., Volume 32 (1998) no. 2, pp. 26-35 (95)

[6] Sabir Gusein-Zade; Ignacio Luengo; Alejandro Melle Hernández Bifurcations and topology of meromorphic germs, Cambridge, 2000 (NATO Sci. Ser. II Math. Phys. Chem.), Volume vol. 21, Kluwer Acad. Publ., Dordrecht (2001), pp. 279-304

[7] Dung Trang Le Some remarks on relative monodromy, Oslo, 1976, Sijthoff and Noordhoff, Alphen aan den Rijn (1977), pp. 397-403

[8] Yutaka Matsui; Kiyoshi Takeuchi Monodromy at infinity of polynomial maps and mixed Hodge modules | arXiv

[9] Michel Raibaut Singularités à lʼinfini et intégration motivique, Bull. Soc. Math. France, Volume 140 (2012) no. 1, pp. 51-100

[10] Michel Raibaut, Motivic Milnor fibers of a rational function, submitted for publication.

[11] Morihiko Saito Mixed Hodge modules, Publ. Res. Inst. Math. Sci., Volume 26 (1990) no. 2, pp. 221-333

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