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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 1999, Volume 225, Pages 168–176
(Mi tm719)
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This article is cited in 2 scientific papers (total in 2 papers)
On Atypical Values and Local Monodromies of Meromorphic Functions
S. M. Gusein-Zadea, I. Luengob, A. Melle-Hernándezb a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b Departamento de Álgebra, Universidad Complutense de Madrid
Abstract:
A meromorphic function on a compact complex analytic manifold defines a $C^\infty$ locally trivial fibration over the complement to a finite set in the projective line $\mathbb{CP}^1$ – the bifurcation set. Loops around points of the bifurcation set give rise to corresponding monodromy transformations of this fibration. We show that the zeta-functions of these monodromy transformations can be expressed in local terms, namely, as integrals of zeta-functions of meromorphic germs with respect to the Euler characteristic. A particular case of meromorphic functions on the projective space $\mathbb{CP}^n$ are those defined by polynomial functions of $n$ variables. We describe some applications of this technique to polynomial functions.
Received in December 1998
Citation:
S. M. Gusein-Zade, I. Luengo, A. Melle-Hernández, “On Atypical Values and Local Monodromies of Meromorphic Functions”, Solitons, geometry, and topology: on the crossroads, Collection of papers dedicated to the 60th anniversary of academician Sergei Petrovich Novikov, Trudy Mat. Inst. Steklova, 225, Nauka, MAIK «Nauka/Inteperiodika», M., 1999, 168–176; Proc. Steklov Inst. Math., 225 (1999), 156–164
Linking options:
https://www.mathnet.ru/eng/tm719 https://www.mathnet.ru/eng/tm/v225/p168
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Abstract page: | 369 | Full-text PDF : | 92 | References: | 80 |
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