Quadratic transforms inside their generic incarnations
Author:
Shreeram S. Abhyankar
Journal:
Proc. Amer. Math. Soc. 140 (2012), 41114126
MSC (2010):
Primary 14A05
Published electronically:
April 12, 2012
MathSciNet review:
2957201
Fulltext PDF
Abstract 
References 
Similar Articles 
Additional Information
Abstract: The generic incarnation of a quadratic transform is obtained by adjoining an indeterminate. This leads to the singularity tree of a generic member of a pencil of curves.
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 S. S. Abhyankar, Historical ramblings in algebraic geometry and related algebra, American Mathematical Monthly, vol. 83 (1976), pages 409448. MR 0401754 (53:5581)
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 S. S. Abhyankar, Lectures on Algebra I, World Scientific, 2006. MR 2253320 (2007k:13001)
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 S. S. Abhyankar, Inversion and Invariance of Characteristic Terms Part I, The Legacy of Alladi Ramakrishnan in the Mathematical Sciences (2010), pages 93168, Springer. MR 2744259 (2012b:14057)
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 S. S. Abhyankar, Dicritical divisors and Jacobian problem, Indian Journal of Pure and Applied Mathematics, vol. 41 (2010), pages 7797. MR 2650101 (2011d:14107)
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 S. S. Abhyankar, Pillars and towers of quadratic transformations, Proceedings of the American Mathematical Society, vol. 139 (2011), pages 30673082. MR 2811263
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Additional Information
Shreeram S. Abhyankar
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
ram@cs.purdue.edu
DOI:
http://dx.doi.org/10.1090/S000299392012115837
PII:
S 00029939(2012)115837
Keywords:
Pencil,
singularity tree,
generic member
Received by editor(s):
May 25, 2011
Published electronically:
April 12, 2012
Communicated by:
Lev Borisov
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
