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arXiv · 1911.00628

Pulling back singularities of codimension one objects

Luis Giraldo·Roland Roeder
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Abstract

We prove that the preimage of a germ of a singular analytic hypersurface under a germ of a finite holomorphic map $g: (\mathbb{C}^n,0) \rightarrow (\mathbb{C}^n,0)$ is again singular. This provides a generalization of previous results of this nature by Ebenfelt-Rothschild [Comm. Anal. Geom. 15 (2007), no. 2, 491-507], Lebl [arXiv:0812.2498], and Denkowski [Manuscripta Math. 149 (2016), no. 1-2, 83-91]. The same statement is proved for pullbacks of singular codimension one holomorphic foliations.

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Luis Giraldo, Roland Roeder. 2019-11-02. Pulling back singularities of codimension one objects. https://doi.org/10.1090/proc/14787

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