Remote Access St. Petersburg Mathematical Journal

St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

Request Permissions   Purchase Content 
 

 

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
Full-text PDF

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in St. Petersburg Mathematical Journal with MSC (2010): 14Q15, 14D05, 58K15, 58K10, 32S20

Retrieve articles in all journals with MSC (2010): 14Q15, 14D05, 58K15, 58K10, 32S20


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