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St. Petersburg Mathematical Journal

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Monodromy zeta-function of a polynomial on a complete intersection, and Newton polyhedra

Author: G. G. Gusev
Translated by: the author
Original publication: Algebra i Analiz, tom 23 (2011), nomer 3.
Journal: St. Petersburg Math. J. 23 (2012), 511-519
MSC (2010): Primary 14Q15, 14D05; Secondary 58K15, 58K10, 32S20
Published electronically: March 2, 2012
MathSciNet review: 2896166
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Abstract | References | Similar Articles | Additional Information

Abstract: For a generic (polynomial) one-parameter deformation of a complete intersection, its monodromy zeta-function is defined. Explicit formulas for this zeta-function in terms of the corresponding Newton polyhedra are obtained in the case where the deformation is nondegenerate with respect to its Newton polyhedra. This result is employed to obtain a formula for the monodromy zeta-function at the origin of a polynomial on a complete intersection, which is an analog of the Libgober-Sperber theorem.

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Additional Information

G. G. Gusev
Affiliation: Moscow Institute of Physics and Technology, Independent University of Moscow, Russia

Keywords: Deformations of polynomials, monodromy zeta-function, Newton polyhedron
Received by editor(s): September 23, 2009
Published electronically: March 2, 2012
Additional Notes: Partially supported by the grants RFBR-10-01-00678, RFBR-08-01-00110-a, RFBR and SU HSE 09-01-12185-off-m, and NOSH-8462.2010.1.
Article copyright: © Copyright 2012 American Mathematical Society

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