Publication: Zeta-functions for germs of meromorphic functions and Newton diagrams
Loading...
Official URL
Full text at PDC
Publication Date
1998-04
Authors
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Verlag
Citations
Exportar
Abstract
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 the germ f around zero and infinity. Based on their previous work [Comment. Math. Helv. 72 (1997), no. 2, 244–256; MR1470090 (98j:32043)] they write down formulas for the zetafunctions of the monodromy operators in terms of partial resolutions of a singularity. In the case where P and Q are non-degenerate relative to their Newton’s diagrams an analog of the formula from [A. N. Varchenko, Invent. Math. 37 (1976), no. 3, 253–262; MR0424806 (54 #12764)] for zeta functions of monodromy operators is obtained. In conclusion, two interesting examples with f = (x3 −xy)/y and f = (xyz +xp +yq +zr)/(xd +yd +zd) are discussed in detail.