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January, 2018 Topology of mixed hypersurfaces of cyclic type
Kazumasa INABA, Masayuki KAWASHIMA, Mutsuo OKA
J. Math. Soc. Japan 70(1): 387-402 (January, 2018). DOI: 10.2969/jmsj/07017538

Abstract

Let $f_{II}({\boldsymbol{z}}, \bar{{\boldsymbol{z}}}) = z_{1}^{a_{1}+b_{1}}\bar{z}_{1}^{b_{1}}z_{2} + \cdots + z_{n-1}^{a_{n-1}+b_{n-1}}\bar{z}_{n-1}^{b_{n-1}}z_{n} + z_{n}^{a_{n}+b_{n}}\bar{z}_{n}^{b_{n}}z_{1}$ be a mixed weighted homogeneous polynomial of cyclic type and $g_{II}({\boldsymbol{z}}) = z_{1}^{a_{1}}z_{2} + \cdots + z_{n-1}^{a_{n-1}}z_{n} + z_{n}^{a_{n}}z_{1}$ be the associated weighted homogeneous polynomial where $a_{j} \geq 1$ and $b_{j} \geq 0$ for $j = 1, \dots, n$. We show that two links $S^{2n-1}_{\varepsilon} \cap f_{II}^{-1}(0)$ and $S^{2n-1}_{\varepsilon} \cap g_{II}^{-1}(0)$ are diffeomorphic and their Milnor fibrations are isomorphic.

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Kazumasa INABA. Masayuki KAWASHIMA. Mutsuo OKA. "Topology of mixed hypersurfaces of cyclic type." J. Math. Soc. Japan 70 (1) 387 - 402, January, 2018. https://doi.org/10.2969/jmsj/07017538

Information

Published: January, 2018
First available in Project Euclid: 26 January 2018

zbMATH: 06859857
MathSciNet: MR3750281
Digital Object Identifier: 10.2969/jmsj/07017538

Subjects:
Primary: 14J17
Secondary: 14J70 , 58K05

Keywords: Milnor fibration , polar weighted homogeneous

Rights: Copyright © 2018 Mathematical Society of Japan

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Vol.70 • No. 1 • January, 2018
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