Journal of the Mathematical Society of Japan

Whitney regularity and Thom condition for families of non-isolated mixed singularities

Christophe EYRAL and Mutsuo OKA

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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.

Article information

J. Math. Soc. Japan, Volume 70, Number 4 (2018), 1305-1336.

Received: 1 March 2017
First available in Project Euclid: 27 July 2018

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Zentralblatt MATH identifier

Primary: 14J70: Hypersurfaces 14J17: Singularities [See also 14B05, 14E15] 32S15: Equisingularity (topological and analytic) [See also 14E15] 32S25: Surface and hypersurface singularities [See also 14J17]

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


EYRAL, Christophe; OKA, Mutsuo. Whitney regularity and Thom condition for families of non-isolated mixed singularities. J. Math. Soc. Japan 70 (2018), no. 4, 1305--1336. doi:10.2969/jmsj/77437743.

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