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

DOI:
https://doi.org/10.1090/S1061-0022-2012-01205-7

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

Email:
gusev@mccme.ru

DOI:
https://doi.org/10.1090/S1061-0022-2012-01205-7

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