On the monodromy at isolated singularities of weighted homogeneous polynomials

Author:
Benjamin G. Cooper

Journal:
Trans. Amer. Math. Soc. **269** (1982), 149-166

MSC:
Primary 32C40; Secondary 14B05

MathSciNet review:
637033

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Abstract: Assume is a weighted homogeneous polynomial with isolated singularity, and define by . If the monomials of are algebraically independent, then the closure of in admits a deformation into the subset where each monomial of has nonnegative real values. For the polynomial , is a cell complex of dimension , invariant under a characteristic map of the fibration , and the inclusion induces isomorphisms in homology. To compute the homology of the link it thus suffices to calculate the action of on . Let . Let be the weights associated with , satisfying for and . Let , , . Then and .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0637033-X

Keywords:
Isolated singularity,
weighted homogeneous polynomial,
Milnor fibre,
monodromy

Article copyright:
© Copyright 1982
American Mathematical Society