A geometric description of the monodromy of Brieskorn-Pham polynomials

Journal of Singularities
volume 22 (2020), 180-189

Received: 2 April 2019. Received in revised form: 23 December 2019.

DOI: 10.5427/jsing.2020.22k

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Abstract:

We give an explicit construction of Lê's vanishing polyhedra for a Brieskorn-Pham polynomial f. Then we use it to give a geometric description of the monodromy associated to f. It allows us to write the matrix that determines the induced algebraic monodromy. In particular, this provides another proof for the Brieskorn-Pham theorem, which says that the characteristic polynomial associated to the monodromy of f is given by Δ(t) = Π(t- ω_1ω_2...ω_n), where each ω_j ranges over all a_j-th roots of unity other than 1.

Author(s) information:

Aurélio Menegon
Universidade Federal da Paraíba
Departamento de Matemática
CEP 58051-900, João Pessoa - PB, Brazil
email: aurelio@mat.ufpb.br