MILNOR FIBERS OVER SINGULAR TORIC VARIETIES AND NEARBY CYCLE SHEAVES

YUTAKA MATSUI; KIYOSHI TAKEUCHI

doi:10.2748/tmj/1303219938

Tohoku Mathematical Journal, Second Series

Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735

MILNOR FIBERS OVER SINGULAR TORIC VARIETIES AND NEARBY CYCLE SHEAVES

YUTAKA MATSUI, KIYOSHI TAKEUCHI

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Keywords: Milnor fibers, Toric varieties, monodromy zeta functions

JOURNAL FREE ACCESS

2011 Volume 63 Issue 1 Pages 113-136

DOI https://doi.org/10.2748/tmj/1303219938

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Abstract

We apply sheaf-theoretical methods to monodromy zeta functions of Milnor fibrations. Classical formulas due to Kushnirenko, Varchenko and Oka, etc. on polynomials over the complex affine space will be generalized to polynomial functions over any toric variety. Moreover our results enable us to calculate the monodromy zeta functions of any constructible sheaf.

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