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Algebraic theory of dicritical divisors

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Publication:3108514
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DOI10.1353/ajm.2011.0045zbMath1232.13012OpenAlexW2163020133MaRDI QIDQ3108514

Shreeram S. Abhyankar, I. Luengo Velasco

Publication date: 4 January 2012

Published in: American Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1353/ajm.2011.0045


zbMATH Keywords

regular local ringvaluation ringdicritical divisorquadratic transformation, Newton polygon


Mathematics Subject Classification ID

Jacobian problem (14R15) Rational and birational maps (14E05) Surfaces and higher-dimensional varieties (14J99) Valuation rings (13F30) Birational geometry (14E99)


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Dicriticals of pencils and Dedekind's Gauss lemma ⋮ Existence of dicritical divisors revisited ⋮ High-school algebra of the theory of dicritical divisors: Atypical fibers for special pencils and polynomials ⋮ Rees valuations ⋮ Dicritical divisors after S.S. Abhyankar and I. Luengo ⋮ Analytic theory of curvettes and dicriticals ⋮ Multiplicities of jumping points for mixed multiplier ideals ⋮ Pillars and towers of quadratic transformations ⋮ More about dicriticals ⋮ Spiders and multiplicity sequences ⋮ Algebraic theory of curvettes and dicriticals ⋮ Generic incarnations of quadratic transforms



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