Monodromy zeta-functions of deformations and Newton diagrams
نویسندگان
چکیده
منابع مشابه
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 the deformation is non-degenerate with respect to its Newton diagram.
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By using sheaf-theoretical methods such as constructible sheaves, we generalize the formula of Libgober-Sperber [15] concerning the zeta functions of monodromy at infinity of polynomial maps into various directions. In particular, some formulas for the zeta functions of global monodromy along the fibers of bifurcation points of polynomial maps will be obtained.
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For a germ of a meromorphic function f = P Q , we offer notions of the mono-dromy operators at zero and at infinity. If the holomorphic functions P and Q are non-degenerated with respect to their Newton diagrams, we give an analogue of the formula of Varchenko for the zeta-functions of these monodromy operators. A polynomial f of (n + 1) complex variables of degree d determines a meromorphic fu...
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For an analytic in σ ∈ (C, 0) family Pσ of polynomials in n variables there is defined a monodromy transformation h of the zero level set Vσ = {Pσ = 0} for σ 6= 0 small enough. The zeta function of this monodromy transformation is written as an integral with respect to the Euler characteristic of the corresponding local data. This leads to a study of deformations of holomorphic germs and their ...
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ژورنال
عنوان ژورنال: Revista Matemática Complutense
سال: 2009
ISSN: 1988-2807,1139-1138
DOI: 10.5209/rev_rema.2009.v22.n2.16282