Tohoku Mathematical Journal

Milnor fibers over singular toric varieties and nearby cycle sheaves

Yutaka Matsui and Kiyoshi Takeuchi

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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.

Article information

Tohoku Math. J. (2), Volume 63, Number 1 (2011), 113-136.

First available in Project Euclid: 19 April 2011

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Zentralblatt MATH identifier

Primary: 32S55: Milnor fibration; relations with knot theory [See also 57M25, 57Q45]
Secondary: 32S60: Stratifications; constructible sheaves; intersection cohomology [See also 58Kxx] 32S40: Monodromy; relations with differential equations and D-modules 14M25: Toric varieties, Newton polyhedra [See also 52B20] 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry) [See also 06A11, 13F20, 13Hxx]

Milnor fibers Toric varieties monodromy zeta functions


Matsui, Yutaka; Takeuchi, Kiyoshi. Milnor fibers over singular toric varieties and nearby cycle sheaves. Tohoku Math. J. (2) 63 (2011), no. 1, 113--136. doi:10.2748/tmj/1303219938.

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