Abhyankar's Work on Dicritical Divisors
William Heinzer, David Shannon
TL;DR
This paper reviews Abhyankar's contributions to dicritical divisors, exploring their algebraic properties and related concepts like local quadratic transforms, near points, and Rees valuation rings.
Contribution
It provides a detailed analysis of Abhyankar's work on dicritical divisors and connects it with related algebraic structures and valuation theory.
Findings
Clarifies the algebraic structure of dicritical divisors
Links dicritical divisors to Rees valuation rings and local quadratic transforms
Highlights the significance of Abhyankar's work in valuation theory
Abstract
We discuss the work of Abhyankar on dicritical divisors with a special focus on the algebraic aspects of this work. We also discuss related work on local quadratic transforms, infinitely near points and Rees valuation rings of an ideal.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Algebraic Geometry and Number Theory · Polynomial and algebraic computation