Étoiles and valuations (Q338228)
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scientific article; zbMATH DE number 6647820
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Étoiles and valuations |
scientific article; zbMATH DE number 6647820 |
Statements
Étoiles and valuations (English)
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4 November 2016
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The author develops the theory of étoiles on complex analytic spaces due to [\textit{H. Hironaka}, Astérisque 7--8, 415--440 (1974; Zbl 0287.14006)] in the context of valuation theory. In particular, he shows that \textit{S. Abhyankar}'s inequality holds [Am. J. Math. 78, 321--348 (1956; Zbl 0074.26301)]. He also proves a regularization theorem for complex analytic morphisms, states the principal theorem for local monomialization of complex analytic spaces along an étoile (see [\textit{S. D. Cutkosky}, Adv. Math. 307, 833--902 (2017; Zbl 1356.32011)]), and so on.
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valuation theory
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Abhyankar's inequality
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regularization theorem
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analytic maps
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local blowups
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étoile
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voûte étoilée
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local monomial transformation
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local monomialization
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