Lipschitz regular complex algebraic sets are smooth

Birbrair, L.; Fernandes, A.; Lê, D.; Sampaio, J.

doi:10.1090/proc/12783

Lipschitz regular complex algebraic sets are smooth
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by L. Birbrair, A. Fernandes, D. T. Lê and J. E. Sampaio PDF

Proc. Amer. Math. Soc. 144 (2016), 983-987 Request permission

Abstract:

A classical theorem of Mumford implies that a topologically regular complex algebraic surface in $\mathbb {C}^3$ with an isolated singular point is smooth. We prove that any Lipschitz regular complex algebraic set is smooth. No restriction on the dimension and no restriction on the singularity to be isolated is needed.

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