Multiple point spaces of finite holomorphic maps

2015/09/16 by J. J. Nuño‐Ballesteros, Nuño-Ballesteros, J. J., Guillermo Peñafort Sanchis +1 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1509.04990

Abstract

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.

Cited by

• A Lê-Greuel type formula for the image Milnor number
• Lipschitz geometry of the image of finite mappings
• An algorithm to compute a presentation of pushforward modules

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