Tohoku Mathematical Journal
2017
March
SECOND SERIES VOL. 69, NO. 1

Tohoku Math. J.
69 (2017), 85-111

Title ON LINEAR DEFORMATIONS OF BRIESKORN SINGULARITIES OF TWO VARIABLES INTO GENERIC MAPS

Author Kazumasa Inaba, Masaharu Ishikawa, Masayuki Kawashima and Tat Thang Nguyen

(Received December 24, 2014, revised May 22, 2015)
Abstract. In this paper, we study deformations of Brieskorn polynomials of two variables obtained by adding linear terms consisting of the conjugates of complex variables and prove that the deformed polynomial maps have only indefinite fold and cusp singularities in general. We then estimate the number of cusps appearing in such a deformation. As a corollary, we show that a deformation of a complex Morse singularity with real linear terms has only indefinite folds and cusps in general and the number of cusps is 3.

Mathematics Subject Classification. Primary 57R45; Secondary 58C27, 14B05.
Key words and phrases. Stable map, higher differential, mixed polynomial.

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