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

@article{Gusev2012MonodromyZO,
  title={Monodromy zeta-function of a polynomial on a complete intersection and Newton polyhedra},
  author={Gleb Gusev},
  journal={arXiv: Algebraic Geometry},
  year={2012}
}
  • Gleb Gusev
  • Published 2012
  • Mathematics
  • arXiv: Algebraic Geometry
For a generic (polynomial) one-parameter deformation of a complete intersection, there is defined its monodromy zeta-function. We provide explicit formulae for this zeta-function in terms of the corresponding Newton polyhedra in the case the deformation is non-degenerate with respect to its Newton polyhedra. Using this result we obtain the 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

SHOWING 1-10 OF 16 REFERENCES
Monodromy zeta functions at infinity, Newton polyhedra and constructible sheaves
By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober–Sperber concerning the zeta functions of monodromy at infinity of polynomial maps into variousExpand
Monodromy zeta-functions of deformations and Newton diagrams
For a one-parameter deformation of an analytic complex function germ of several variables, there is defined its monodromy zeta-function. We give a Varchenko type formula for this zeta-function if theExpand
Deformations of polynomials and their zeta-functions
For an analytic in σ ∈ (ℂ 0) family Pσ of polynomials in n variables a monodromy transformation h of the zero level set Vσ={Pσ=0} for sufficiently small σ ≠ 0 is defined. The zeta-function of thisExpand
Deformations of polynomials and their zeta functions
For an analytic family P_s of polynomials in n variables (depending on a complex number s, and defined in a neighborhood of s = 0), there is defined a monodromy transformation h of the zero level setExpand
Newton polyhedra and toroidal varieties
The toroidal compactification (C~0)~f ~ plays the same role as the projective compactification ~ P ~ in the classical case. Toroidal varieties are well known [2, 3]. It is almost as easy to handleExpand
THEOREMS ON THE TOPOLOGICAL EQUISINGULARITY OF FAMILIES OF ALGEBRAIC VARIETIES AND FAMILIES OF POLYNOMIAL MAPPINGS
In this paper we consider families of complex or real algebraic varieties. We prove that for almost all values of the parameters both the topology of the variety and its position in space will be theExpand
Zeta functions for germs of meromorphic functions, and Newton diagrams
Let f be a meromorphic function germ on (Cn+1, 0); that is, f = P/Q, where P,Q: (Cn+1, 0)! (C, 0) are holomorphic germs. The authors introduce a notion of Milnor fibers and monodromy operators of theExpand
Deformations of polynomials, boundary singularities and monodromy
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is relatedExpand
On the zeta function of monodromy of a polynomial map
© Foundation Compositio Mathematica, 1995, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditionsExpand
Monodromy zeta-function at infinity
  • Newton polyhedra, and constructible sheaves, Math. Z., 268
  • 2011
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