TL;DR
This paper explores properties of 'etoiles' and their valuations in complex analytic spaces, demonstrating Abhyankar's inequality, providing examples of unusual valuation behavior, and proving a regularization theorem for morphisms.
Contribution
It introduces new properties of 'etoiles' and valuations, and establishes a regularization theorem for complex analytic morphisms.
Findings
Abhyankar's inequality holds for 'etoiles' and valuations
Examples of pathological valuation behavior are provided
A regularization theorem for complex analytic morphisms is proved
Abstract
We establish some properties of \'etoiles and associated valuations over complex analytic spaces, showing that Abhyankar's inequality holds. We give some examples of pathological behavior of these valuations. We prove a regularization theorem for complex analytic morphisms.
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Taxonomy
TopicsMeromorphic and Entire Functions · Algebraic Geometry and Number Theory · Advanced Mathematical Identities