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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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More about dicriticals
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by Shreeram S. Abhyankar PDF
Proc. Amer. Math. Soc. 139 (2011), 3083-3097 Request permission

Abstract:

This paper attempts to characterize the dicritical set of a rational function which generates a special pencil at a simple point of an algebraic or arithmetical surface.
References
  • Shreeram Abhyankar, On the valuations centered in a local domain, Amer. J. Math. 78 (1956), 321–348. MR 82477, DOI 10.2307/2372519
  • Shreeram Abhyankar, Ramification theoretic methods in algebraic geometry, Annals of Mathematics Studies, No. 43, Princeton University Press, Princeton, N.J., 1959. MR 0105416, DOI 10.1515/9781400881390
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  • S. S. Abhyankar, Lectures on algebra. Vol. I, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2006. MR 2253320, DOI 10.1142/9789812773449
  • S. S. Abhyankar, Inversion and Invariance of Characteristic Terms, Part I, Developments in Mathematics, Springer, 2010.
  • Shreeram S. Abhyankar, Dicritical divisors and Jacobian problem, Indian J. Pure Appl. Math. 41 (2010), no. 1, 77–97. MR 2650101, DOI 10.1007/s13226-010-0017-x
  • S. S. Abhyankar, Pillars and Towers of Quadratic Transformations, Proceedings of the American Mathematical Society, to appear.
  • S. S. Abhyankar and W. J. Heinzer, Existence of dicritical divisors, American Journal of Mathematics, to appear.
  • S. S. Abhyankar and I. Luengo, Algebraic theory of dicritical divisors, American Journal of Mathematics, to appear.
  • Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, Graduate Texts in Mathematics, Vol. 29, Springer-Verlag, New York-Heidelberg, 1975. Reprint of the 1960 edition. MR 0389876
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Additional Information
  • Shreeram S. Abhyankar
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email: ram@cs.purdue.edu
  • Received by editor(s): January 30, 2010
  • Received by editor(s) in revised form: August 7, 2010
  • Published electronically: January 24, 2011
  • Communicated by: Bernd Ulrich
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3083-3097
  • MSC (2010): Primary 14A05
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10732-9
  • MathSciNet review: 2811264