Non-compact Newton boundary and Whitney equisingularity for non-isolated singularities

2015/12/14 by Christophe Eyral, Eyral, Christophe, Mutsuo Oka +1 · 4 citations
Mathematics · #14J17 #14J70 #32S15 #32S25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J17 #msc:14J70 #msc:32S15 #msc:32S25

paper · pdf · doi:10.48550/arxiv.1512.04248

arxiv created 2015/12/14 · arxiv updated 2015/12/15

Abstract

In an unpublished lecture note, J. Briançon observed that if \f_t\ is a family of isolated complex hypersurface singularities such that the Newton boundary of f_t is independent of t and f_t is non-degenerate, then the corresponding family of hypersurfaces \f_t^-1(0)\ is Whitney equisingular (and hence topologically equisingular). A first generalization of this assertion to families with non-isolated singularities was given by the second author under a rather technical condition. In the present paper, we give a new generalization under a simpler condition.

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