Contents Online
Methods and Applications of Analysis
Volume 24 (2017)
Number 2
Special issue dedicated to Henry B. Laufer on the occasion of his 70th birthday: Part 2
Guest Editors: Stephen S.-T. Yau (Tsinghua University, China); Gert-Martin Greuel (University of Kaiserslautern, Germany); Jonathan Wahl (University of North Carolina, USA); Rong Du (East China Normal University, China); Yun Gao (Shanghai Jiao Tong University, China); and Huaiqing Zuo (Tsinghua University, China)
Equisingular and equinormalizable deformations of isolated non-normal singularities
Pages: 215 – 276
DOI: https://dx.doi.org/10.4310/MAA.2017.v24.n2.a3
Author
Abstract
We present new results on equisingularity and equinormalizability of families with isolated non–normal singularities (INNS) of arbitrary dimension. We define a $\delta$-invariant and a $\mu$-invariant for an INNS and prove necessary and sufficient numerical conditions for equinormalizability and weak equinormalizability using $\delta$ and $\mu$. For families of generically reduced curves, we investigate the topological behavior of the Milnor fibre and characterize topological triviality of such families. Finally we state some open problems and conjectures. In addition we give a survey of classical results about equisingularity and equinormalizability so that the article may be useful as a reference source.
Keywords
equisingularity, Milnor number, $\delta$-invariant, isolated non-normal singularities, simultaneous normalization, topological triviality
2010 Mathematics Subject Classification
14B05, 14B07, 14B10, 14H20, 32B10, 32C20, 32S05, 32S15, 32S25, 32S30
Received 24 January 2017
Accepted 1 July 2017
Published 3 January 2018