Pulling back singularities of codimension one objects
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- by Luis Giraldo and Roland K. W. Roeder PDF
- Proc. Amer. Math. Soc. 148 (2020), 1207-1217 Request permission
Abstract:
We prove that the preimage of a germ of a singular analytic hypersurface under a germ of a finite holomorphic map $g: (\mathbb {C}^n, \mathbf{0}) \rightarrow (\mathbb {C}^n, \mathbf{0})$ 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 preprint https://arxiv.orglabs/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.References
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Additional Information
- Luis Giraldo
- Affiliation: Departmento de Álgebra, Geometría y Topología and IMI, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, Ciudad Universitaria, Plaza de Ciencias 3, 28040 Madrid, Spain
- MR Author ID: 601346
- Email: luis.giraldo@mat.ucm.es
- Roland K. W. Roeder
- Affiliation: Department of Mathematical Sciences, Indiana University–Purdue University Indianapolis, LD Building, Room 224Q, 402 North Blackford Street, Indianapolis, Indiana 46202-3267
- MR Author ID: 718580
- Email: rroeder@math.iupui.edu
- Received by editor(s): May 10, 2019
- Received by editor(s) in revised form: July 23, 2019
- Published electronically: October 18, 2019
- Additional Notes: Part of this research was done while the first author was visiting the Department of Mathematics of Indiana University at Bloomington, supported by the “Salvador de Madariaga” grant no. PRX18/00404 funded by the Spanish Government. He was also partially supported by the research grants MTM2015-63612-P and PGC2018-098321-B-I00, of the Spanish Government.
The second author was supported by NSF grant DMS-1348589. - Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 148 (2020), 1207-1217
- MSC (2010): Primary 32SXX, 32S65, 14J17
- DOI: https://doi.org/10.1090/proc/14787
- MathSciNet review: 4055948