Tohoku Mathematical Journal
2011
March
SECOND SERIES VOL. 63, NO. 1

Tohoku Math. J.
63 (2011), 113-136

Title MILNOR FIBERS OVER SINGULAR TORIC VARIETIES AND NEARBY CYCLE SHEAVES

Author Yutaka Matsui and Kiyoshi Takeuchi

(Received March 11, 2010, revised August 17, 2010)
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.

2000 Mathematics Subject Classification. Primary 32S55; Secondary 32S60, 32S40, 14M25, 52B20.
Key words and phrases. Milnor fibers, Toric varieties, monodromy zeta functions.

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