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Whitney regularity and Thom condition for families of non-isolated mixed singularities (1607.03741v1)
Published 13 Jul 2016 in math.AG
Abstract: We investigate the equisingularity question for $1$-parameter deformation families of mixed polynomial functions $f_t(\mathbf{z},\bar{\mathbf{z}})$ 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.