Volume 16, issue 1 (2012)

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Generalized Monodromy Conjecture in dimension two

András Némethi and Willem Veys

Geometry & Topology 16 (2012) 155–217
Bibliography
1 D Abramovich, K Karu, K Matsuki, J Włodarczyk, Torification and factorization of birational maps, J. Amer. Math. Soc. 15 (2002) 531 MR1896232
2 N A’Campo, La fonction zêta d'une monodromie, Comment. Math. Helv. 50 (1975) 233 MR0371889
3 E Artal Bartolo, P Cassou-Noguès, I Luengo, A Melle Hernández, Monodromy conjecture for some surface singularities, Ann. Sci. École Norm. Sup. 35 (2002) 605 MR1981174
4 E Artal Bartolo, P Cassou-Noguès, I Luengo, A Melle Hernández, Quasi-ordinary power series and their zeta functions, Mem. Amer. Math. Soc. 178, no. 841, Amer. Math. Soc. (2005) MR2172403
5 D Barlet, Contribution effective de la monodromie aux développements asymptotiques, Ann. Sci. École Norm. Sup. 17 (1984) 293 MR760679
6 N Budur, M Mustaţă, Z Teitler, The monodromy conjecture for hyperplane arrangements, Geom. Dedicata 153 (2011) 131 MR2819667
7 J Denef, F Loeser, Caractéristiques d'Euler–Poincaré, fonctions zêta locales et modifications analytiques, J. Amer. Math. Soc. 5 (1992) 705 MR1151541
8 J Denef, F Loeser, Motivic Igusa zeta functions, J. Algebraic Geom. 7 (1998) 505 MR1618144
9 D Eisenbud, W Neumann, Three-dimensional link theory and invariants of plane curve singularities, Annals of Math. Studies 110, Princeton Univ. Press (1985) MR817982
10 M Kashiwara, Vanishing cycle sheaves and holonomic systems of differential equations, from: "Algebraic geometry (Tokyo/Kyoto, 1982)" (editors M Raynaud, T Shioda), Lecture Notes in Math. 1016, Springer (1983) 134 MR726425
11 H B Laufer, Normal two-dimensional singularities, Annals of Math. Studies 71, Princeton Univ. Press (1971) MR0320365
12 A Lemahieu, L Van Proeyen, Monodromy conjecture for nondegenerate surface singularities, Trans. Amer. Math. Soc. 363 (2011) 4801 MR2806692
13 A Lemahieu, W Veys, Zeta functions and monodromy for surfaces that are general for a toric idealistic cluster, Int. Math. Res. Not. 2009 (2009) 11 MR2471295
14 F Loeser, Fonctions d'Igusa $p$–adiques et polynômes de Bernstein, Amer. J. Math. 110 (1988) 1 MR926736
15 F Loeser, Fonctions d'Igusa $p$–adiques, polynômes de Bernstein, et polyèdres de Newton, J. Reine Angew. Math. 412 (1990) 75 MR1079002
16 B Malgrange, Polynômes de Bernstein–Sato et cohomologie évanescente, from: "Analysis and topology on singular spaces, II, III (Luminy, 1981)", Astérisque 101, Soc. Math. France (1983) 243 MR737934
17 A Némethi, “Weakly” elliptic Gorenstein singularities of surfaces, Invent. Math. 137 (1999) 145 MR1703331
18 A Némethi, W D Neumann, A Pichon, Principal analytic link theory in homology sphere links, from: "Topology of algebraic varieties and singularities" (editors J I Cogolludo-Agustín, E Hironaka), Contemp. Math. 538, Amer. Math. Soc. (2011) 377 MR2777831
19 A Némethi, W Veys, Monodromy eigenvalues are induced by poles of zeta functions: the irreducible curve case, Bull. Lond. Math. Soc. 42 (2010) 312 MR2601558
20 W D Neumann, J Wahl, Universal abelian covers of surface singularities, from: "Trends in singularities" (editors A Libgober, M Tibăr), Trends Math., Birkhäuser (2002) 181 MR1900786
21 W D Neumann, J Wahl, Complex surface singularities with integral homology sphere links, Geom. Topol. 9 (2005) 757 MR2140992
22 W D Neumann, J Wahl, The end curve theorem for normal complex surface singularities, J. Eur. Math. Soc. 12 (2010) 471 MR2608949
23 T Okuma, Another proof of the end curve theorem for normal surface singularities, J. Math. Soc. Japan 62 (2010) 1 MR2648226
24 B Rodrigues, On the monodromy conjecture for curves on normal surfaces, Math. Proc. Cambridge Philos. Soc. 136 (2004) 313 MR2040577
25 B Rodrigues, W Veys, Poles of zeta functions on normal surfaces, Proc. London Math. Soc. 87 (2003) 164 MR1978573
26 W Veys, Poles of Igusa's local zeta function and monodromy, Bull. Soc. Math. France 121 (1993) 545 MR1254752
27 W Veys, Zeta functions for curves and log canonical models, Proc. London Math. Soc. 74 (1997) 360 MR1425327
28 W Veys, The topological zeta function associated to a function on a normal surface germ, Topology 38 (1999) 439 MR1660317
29 W Veys, Zeta functions and “Kontsevich invariants” on singular varieties, Canad. J. Math. 53 (2001) 834 MR1848509
30 W Veys, Vanishing of principal value integrals on surfaces, J. Reine Angew. Math. 598 (2006) 139 MR2270570
31 W Veys, Monodromy eigenvalues and zeta functions with differential forms, Adv. Math. 213 (2007) 341 MR2331246
32 J Włodarczyk, Toroidal varieties and the weak factorization theorem, Invent. Math. 154 (2003) 223 MR2013783
33 S S T Yau, Hypersurface weighted dual graphs of normal singularities of surfaces, Amer. J. Math. 101 (1979) 761 MR536041