Monodromy conjecture for some surface singularities
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 35 (2002) no. 4, pp. 605-640.
@article{ASENS_2002_4_35_4_605_0,
     author = {Artal Bartolo, E. and Cassou-Nogu\`es, P. and Luengo, I. and Melle Hern\'andez, A.},
     title = {Monodromy conjecture for some surface singularities},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {605--640},
     publisher = {Elsevier},
     volume = {Ser. 4, 35},
     number = {4},
     year = {2002},
     doi = {10.1016/s0012-9593(02)01100-x},
     zbl = {1020.32025},
     mrnumber = {1981174},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/s0012-9593(02)01100-x/}
}
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Artal Bartolo, E.; Cassou-Noguès, P.; Luengo, I.; Melle Hernández, A. Monodromy conjecture for some surface singularities. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 35 (2002) no. 4, pp. 605-640. doi : 10.1016/s0012-9593(02)01100-x. http://www.numdam.org/articles/10.1016/s0012-9593(02)01100-x/

[1] A'Campo N., La fonction zeta d'une monodromie, Comment. Math. Helv. 50 (1975) 233-248. | MR | Zbl

[2] Artal Bartolo E., Forme de Jordan de la monodromie des singularités superisolées de surfaces, Mem. Amer. Math. Soc. 109 (525) (1994). | MR | Zbl

[3] Artal Bartolo E., Sur les couples de Zariski, J. Algebraic Geom. 3 (2) (1994) 223-247. | MR | Zbl

[4] Artal Bartolo E., Cassou-Noguès Pi., Luengo I., Melle-Hernández A., Denef-Loeser zeta function is not a topological invariant, J. London Math. Soc. (2001), to appear. | Zbl

[5] Artal Bartolo E., Luengo I., Melle-Hernández A., On a conjecture of W. Veys, Math. Ann. 317 (2) (2000) 325-327. | MR | Zbl

[6] Denef J., Report on Igusa's local zeta function, Astérisque, 201-203, 1991, Exp. No. 741, Séminaire Bourbaki, Vol. 1990/91, 1992, 359-386. | Numdam | MR | Zbl

[7] Denef J., Loeser F., Caractéristiques d'Euler-Poincaré, fonctions zêta locales et modifications analytiques, J. Amer. Math. Soc. 5 (4) (1992) 705-720. | MR | Zbl

[8] Denef J., Loeser F., Motivic Igusa zeta functions, J. Algebraic Geom. 7 (3) (1998) 505-537. | MR | Zbl

[9] Denef J., Loeser F., Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1) (1999) 201-232. | MR | Zbl

[10] Denef J., Loeser F., Geometry on arc spaces of algebraic varieties, to appear in Proceedings of the Third European Congress of Mathematics, Barcelona 2000, p. 22, math.AG/0006050. | MR | Zbl

[11] Dimca A., On the connectivity of a complex affine hyperserfaces, Topology 29 (1990) 511-514. | MR | Zbl

[12] Dimca A., Némethi A., On the monodromy of complex polynomials, Duke Math. J. 108 (2) (2001) 199-209. | MR | Zbl

[13] Eisenbud D., Neumann W.D., Three-Dimensional Link Theory and Invariance of Plane Curve Singularities, Annals of Mathematics Studies, 110, Princeton University Press, Princeton, NJ, 1985. | MR | Zbl

[14] Esnault H., Fibre de Milnor d'un cône sur une courbe plane singulière, Invent. Math. 68 (3) (1982) 477-496. | MR | Zbl

[15] Gurjar R., Parameswaran A., Open surfaces with non-positive euler characteristic, Compositio Math. 99 (1995) 213-229. | Numdam | MR | Zbl

[16] De Jong A.J., Steenbrink J., Proof of a conjecture of W. Veys, Indag. Math. (N.S.) 6 (1) (1995) 99-104. | MR | Zbl

[17] Kashiwara H., Fonctions rationnelles de type (0,1) sur le plan projectif complexe, Osaka J. Math. 24 (3) (1987) 521-577. | MR | Zbl

[18] Kizuka T., Rational functions of C-type on the two-dimensional complex projective space, Tohoku Math. J. (2) 38 (1) (1986) 123-178. | Zbl

[19] Kojima H., On Veys' conjecture, Indag. Math. (N.S.) 10 (4) (1999) 537-538. | MR | Zbl

[20] Libgober A., Alexander polynomial of plane algebraic curves and cyclic multiple planes, Duke Math. J. 49 (4) (1982) 833-851. | MR | Zbl

[21] Loeser F., Fonctions d'Igusa p-adiques et polynômes de Bernstein, Amer. J. Math. 110 (1) (1988) 1-21. | MR | Zbl

[22] Loeser F., Fonctions d'Igusa p-adiques, polynômes de Bernstein, et polyèdres de Newton, J. Reine Angew. Math. 412 (1990) 75-96. | MR | Zbl

[23] Loeser F., Vaquié M., Le polynôme d'Alexander d'une courbe plane projective, Topology 29 (2) (1990) 163-173. | MR | Zbl

[24] Looijenga E., Motivic measures, Sèminaire Bourbaki, exposé 874, to appear in Asterisque, 2000, p. 25, math.AG/0006220. | Numdam | MR | Zbl

[25] Luengo I., The μ-constant stratum is not smooth, Invent. Math. 90 (1) (1987) 139-152. | Zbl

[26] Rodrigues B., Veys W., Holomorphy of Igusa's and topological zeta functions for homogeneous polynomials, Pacific J. Math., to appear. | MR | Zbl

[27] Siersma D., Variation mappings on singularities with a 1-dimensional critical locus, Topology 30 (3) (1991) 445-469. | MR | Zbl

[28] Stevens J., On the μ-constant stratum and the V-filtration: an example, Math. Z. 201 (1) (1989) 139-144. | Zbl

[29] Veys W., Poles of Igusa's local zeta function and monodromy, Bull. Soc. Math. France 121 (4) (1993) 545-598. | Numdam | MR | Zbl

[30] Veys W., Determination of the poles of the topological zeta function for curves, Manuscripta Math. 87 (4) (1995) 435-448. | MR | Zbl

[31] Veys W., Zeta functions for curves and log canonical models, Proc. London Math. Soc. (3) 74 (2) (1997) 360-378. | MR | Zbl

[32] Veys W., Structure of rational open surfaces with non-positive Euler characteristic, Math. Ann. 312 (1998) 527-548. | MR | Zbl

[33] Veys W., Zeta functions and ‘Konsevitch invariants' on singular varities, Canad. J. Math. 53 (4) (2001) 834-856. | Zbl

[34] Yoshihara H., On plane rational curves, Proc. Japan Acad. Ser. A Math. Sci. 55 (4) (1979) 152-155. | MR | Zbl

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