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

作者：Eyral Christophe^*; Oka Mutsuo

来源：Advances in Mathematics, 2017, 316: 94-113.

DOI：10.1016/j.aim.2017.06.003

• Non-isolated hypersurface
• singularities
• Non-compact Newton boundary
• Uniform local tameness
• Whitney equisingularity

In an unpublished lecture note, J. Briancon observed that if {f(t)} is a family of isolated complex hypersurface singularities such that the Newton boundary of ft is independent of t and ft 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.

• 出版日期2017-8-20