Open Access
October, 2018 Whitney regularity and Thom condition for families of non-isolated mixed singularities
Christophe EYRAL, Mutsuo OKA
J. Math. Soc. Japan 70(4): 1305-1336 (October, 2018). DOI: 10.2969/jmsj/77437743


We investigate the equisingularity question for 1-parameter deformation families of mixed polynomial functions $f_t({\boldsymbol{z}},\bar{{\boldsymbol{z}}})$ from the Newton polygon point of view. We show that if the members $f_t$ of the family satisfy a number of elementary conditions, which can be easily described in terms of the Newton polygon, then the corresponding family of mixed hypersurfaces $f_t^{-1}(0)$ is Whitney equisingular (and hence topologically equisingular) and satisfies the Thom condition.


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Christophe EYRAL. Mutsuo OKA. "Whitney regularity and Thom condition for families of non-isolated mixed singularities." J. Math. Soc. Japan 70 (4) 1305 - 1336, October, 2018.


Received: 1 March 2017; Published: October, 2018
First available in Project Euclid: 27 July 2018

zbMATH: 07009703
MathSciNet: MR3868208
Digital Object Identifier: 10.2969/jmsj/77437743

Primary: 14J17 , 14J70 , 32S15 , 32S25

Keywords: deformation family of mixed singularities , non-compact Newton boundary , strong non-degeneracy , Thom $a_f$ condition , uniform local tameness , Whitney $(b)$-regularity , Whitney equisingularity

Rights: Copyright © 2018 Mathematical Society of Japan

Vol.70 • No. 4 • October, 2018
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