Multiple point spaces of finite holomorphic maps

We show that there exists a unique possible definition, with certain natural properties, of the multiple point space of a holomorphic map between complex manifolds. Our construction coincides with the double point space and the k-th multiple point space for corank one map-germs, due to Mond. We also...

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Bibliographic Details
Published in:arXiv.org 2016-10
Main Authors: Nuño-Ballesteros, J J, Peñafort-Sanchis, G
Format: Article
Language:English
Subjects:
Mathematical analysis
Online Access:Get full text
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Summary:We show that there exists a unique possible definition, with certain natural properties, of the multiple point space of a holomorphic map between complex manifolds. Our construction coincides with the double point space and the k-th multiple point space for corank one map-germs, due to Mond. We also give some interesting properties of the double point space and prove that in many cases it can be computed as the zero locus of certain quotient of ideals.
ISSN:2331-8422