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High-school algebra of the theory of dicritical divisors: atypical fibres for special pencils and polynomials

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Artal Bartolo, Enrique and Luengo Velasco, Ignacio and Melle Hernández, Alejandro (2015) High-school algebra of the theory of dicritical divisors: atypical fibres for special pencils and polynomials. Journal of Algebra and Its Applications, 14 (9). pp. 1-23. ISSN 0219-4988

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0219498815400095


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http://arxiv.org/pdf/1408.0743.pdfOrganisation


Abstract

In this work we deal with dicritical divisors, curvettes and polynomials.These objects have been one of the main research interests of S.S. Abhyanka during his last years. In this work we provide some elementary proofs of some S.S.Abhyankar and I. Luengo results for dicriticals in the framework of forma power series. Based on these ideas we give anconstructive way to find the atypical fibres of a special pencil and give bounds for its number, which are sharper than the existing ones. Finally, we answer a question of J. Gwozdziewicz finding polynomials that reach his bound.


Item Type:Article
Uncontrolled Keywords:Dicritical Divisor, Special Pencil
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:29712
Deposited On:23 Apr 2015 06:41
Last Modified:19 Jan 2016 17:33

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