Special Issue In Honor of Shreeram S. Abhyankar (1930–2012); Guest Editors: S. R. Ghorpade and A. SathayeNo Access
High-school algebra of the theory of dicritical divisors: Atypical fibers for special pencils and polynomials
Abstract
In this work we deal with dicritical divisors, curvettes and polynomials. These objects have been one of the main research interests of Abhyankar during his last years. In this work we provide some elementary proofs of some Abhyankar and Luengo results for dicriticals in the framework of formal power series. Based on these ideas we give a constructive way to find the atypical fibers of a special pencil and give bounds for its number, which are sharper than the existing ones. Finally, we answer a question of Gwoździewicz finding polynomials that reach his bound.
In this work we got a revival of our discussions about dicriticals with Ram.
Dedicated to the memory of S. S. Abhyankar
Keywords:
AMSC: 14A05, 14R15
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