Monodromy of functions on isolated cyclic quotients

✍ Scribed by Mihai Tibăr

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 217 KB
• Volume: 97
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00059-5

✦ Synopsis

We study two important invariants of the monodromy of a function on an isolated cyclic quotient (C n /G, 0), where G is a finite cyclic group: the Lefschetz number and the zeta-function. Our approach relies on a certain "good" toric modification of C n inducing a toric resolution of the cyclic quotient. We prove that the Lefschetz number has a sum decomposition into Lefschetz numbers of well-defined weighted-homogeneous "pieces" of the initial function, the weights depending only on the group action. We define a class of nondegenerate functions and prove for them a zeta-function formula, using Varchenko's approach via the Newton polyhedron.