Motivic Milnor fiber at infinity and composition with a non-degenerate polynomial
- [1] Université de Nice, Laboratoire Jean-Alexandre Dieudonné, Parc Valrose, 06108 NICE Cedex 2, France University of Leuven, Department of Mathematics, Celestijnenlaan 200 B,B-3001 Leuven (Heverlee), Belgium
Annales de l’institut Fourier (2012)
- Volume: 62, Issue: 5, page 1943-1981
- ISSN: 0373-0956
Access Full Article
topAbstract
topHow to cite
topReferences
top- Franziska Bittner, On motivic zeta functions and the motivic nearby fiber, Math. Z. 249 (2005), 63-83 Zbl1085.14020MR2106970
- Pierre Deligne, Théorie de Hodge. III, Inst. Hautes Études Sci. Publ. Math. (1974), 5-77 Zbl0237.14003MR498552
- Jan Denef, François Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), 201-232 Zbl0928.14004MR1664700
- Jan Denef, François Loeser, Geometry on arc spaces of algebraic varieties, European Congress of Mathematics, Vol. I (Barcelona, 2000) 201 (2001), 327-348, Birkhäuser, Basel Zbl1079.14003MR1905328
- A. Douai, C. Sabbah, Gauss-Manin systems, Brieskorn lattices and Frobenius structures. I, Ann. Inst. Fourier (Grenoble) 53 (2003), 1055-1116 Zbl1079.32016MR2033510
- Antoine Douai, Claude Sabbah, Gauss-Manin systems, Brieskorn lattices and Frobenius structures. II, (2004), 1-18 Zbl1079.32017
- William Fulton, Intersection theory, 2 (1998), Springer-Verlag, Berlin Zbl0541.14005MR1644323
- Gil Guibert, Espaces d’arcs et invariants d’Alexander, Comment. Math. Helv. 77 (2002), 783-820 Zbl1046.14008MR1949114
- Gil Guibert, François Loeser, Michel Merle, Nearby cycles and composition with a nondegenerate polynomial, Int. Math. Res. Not. (2005), 1873-1888 Zbl1093.14032MR2171196
- Gil Guibert, François Loeser, Michel Merle, Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of Steenbrink, Duke Math. J. 132 (2006), 409-457 Zbl1173.14301MR2219263
- Heisuke Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203 ; ibid. (2) 79 (1964), 205-326 Zbl0122.38603MR199184
- A. G. Kouchnirenko, Polyèdres de Newton et nombres de Milnor, Invent. Math. 32 (1976), 1-31 Zbl0328.32007MR419433
- François Loeser, Seattle lectures on motivic integration, Algebraic geometry—Seattle 2005. Part 2 80 (2009), 745-784, Amer. Math. Soc., Providence, RI Zbl1181.14017MR2483954
- Eduard Looijenga, Motivic measures, Astérisque (2002), 267-297 Zbl0996.14011MR1886763
- Yutaka Matsui, Kiyoshi Takeuchi, Monodromy at infinity of polynomial map and mixed Hodge modules, arXiv :0912.5144v5 Zbl1314.32044
- Yutaka Matsui, Kiyoshi Takeuchi, Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves, Math. Z. 268 (2011), 409-439 Zbl1264.14005MR2805442
- Frédéric Pham, Vanishing homologies and the variable saddlepoint method, Singularities, Part 2 (Arcata, Calif., 1981) 40 (1983), 319-333, Amer. Math. Soc., Providence, RI Zbl0519.49026MR713258
- Michel Raibaut, Fibre de Milnor motivique à l’infini, C. R. Math. Acad. Sci. Paris 348 (2010), 419-422 Zbl1195.14028MR2607031
- Michel Raibaut, Singularités à l’infini et intégration motivique, Thèse, Université Nice Sophia Antipolis (2010) Zbl1195.14028
- Michel Raibaut, Singularités à l’infini et intégration motivique, Bull. Soc. Math. France 140 (2012), 51-100 Zbl1266.14012MR2903771
- Claude Sabbah, Monodromy at infinity and Fourier transform, Publ. Res. Inst. Math. Sci. 33 (1997), 643-685 Zbl0920.14003MR1489993
- Morihiko Saito, Mixed Hodge modules, Publ. Res. Inst. Math. Sci. 26 (1990), 221-333 Zbl0727.14004MR1047415
- Joseph Steenbrink, Steven Zucker, Variation of mixed Hodge structure. I, Invent. Math. 80 (1985), 489-542 Zbl0626.14007MR791673