# zbMATH — the first resource for mathematics

A motivic Milnor fiber at infinity. (Fibre de Milnor motivique à l’infini.) (French) Zbl 1195.14028
For a regular function defined on a smooth complex algebraic variety, the author introduces a motivic Milnor fiber at infinity. This can be computed using compactifications of the function, but is independent of the choice of such a compactification. Explicit computations are given for a non-degenerate Laurent polynomial with respect to its Newton polyhedra at infinity.
Related work was recently done by Y. Matsui and K. Takeuchi.

##### MSC:
 14F42 Motivic cohomology; motivic homotopy theory 32S55 Milnor fibration; relations with knot theory
##### Keywords:
motivic Milnor fiber at infinity; Laurent polynomial
Full Text:
##### References:
 [1] Denef, J.; Loeser, F., Geometry on arc spaces of algebraic varieties, (), 327-348 · Zbl 1079.14003 [2] Denef, J.; Loeser, F., Motivic igusa zeta functions, J. algebraic geom., 7, 505-537, (1998) · Zbl 0943.14010 [3] García López, R.; Némethi, A., Hodge numbers attached to a polynomial map, Ann. inst. Fourier (Grenoble), 49, 1547-1579, (1999) · Zbl 0944.32029 [4] Guibert, G., Espaces d’arcs et invariants d’Alexander, Comment. math. helv., 77, 783-820, (2002) · Zbl 1046.14008 [5] Guibert, G.; Loeser, F.; Merle, M., Nearby cycles and composition with a nondegenerate polynomial, Internat. math. res. notices, 31, 1873-1888, (2005) · Zbl 1093.14032 [6] Guibert, G.; Loeser, F.; Merle, M., Iterated vanishing cycles, convolution, and a motivic analogue of a conjecture of steenbrink, Duke math. J., 132, 409-457, (2006) · Zbl 1173.14301 [7] Kouchnirenko, A.G., Polyèdres de Newton et nombres de Milnor, Invent. math., 32, 1-31, (1976) · Zbl 0328.32007 [8] Matsui, Y.; Takeuchi, K., Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves · Zbl 1264.14005 [9] Matsui, Y.; Takeuchi, K., Monodromy at infinity of polynomial map and mixed Hodge modules [10] Némethi, A.; Sabbah, C., Semicontinuity of the spectrum at infinity, Abh. math. sem. univ. Hamburg, 69, 25-35, (1999) · Zbl 0973.32014 [11] Peters, C.A.; Steenbrink, J.H.M., Mixed Hodge structures, (2008), Springer-Verlag [12] Pham, F., Vanishing homologies and the n variable saddlepoint method, (), 319-333 [13] Sabbah, C., Monodromy at infinity and Fourier transform, Publ. res. inst. math. sci., 33, 643-685, (1997) · Zbl 0920.14003 [14] Saito, M., Mixed Hodge modules, Publ. res. inst. math. sci., 26, 221-333, (1990) · Zbl 0727.14004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.