St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

   
 

 

Newtonian and affine classifications of irreducible cubics


Author: A. B. Korchagin
Translated by: the author
Original publication: Algebra i Analiz, tom 24 (2012), nomer 5.
Journal: St. Petersburg Math. J. 24 (2013), 759-781
MSC (2010): Primary 14P25, 14R05, 14H50; Secondary 51N10, 01A45, 32Q57
Published electronically: July 24, 2013
MathSciNet review: 3087822
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Abstract | References | Similar Articles | Additional Information

Abstract: The equivalence classes of Newton's classification of irreducible cubics are described in terms of families of standard equations. An affine classification of irreducible cubics is given.


References [Enhancements On Off] (What's this?)

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  • 2. F. Klein, Lectures on mathematics, The Evanston Colloquium with a preface by A. Ziwet, Merchant Books, 2007, 124 pp.
  • 3. A. S. Smogorževs′kiĭ and E. S. Stolova, Spravochnik po teorii ploskikh krivykh tretego poryadka, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0125500
  • 4. Anatoly B. Korchagin and David A. Weinberg, Quadric, cubic and quartic cones, Rocky Mountain J. Math. 35 (2005), no. 5, 1627–1656. MR 2206027, 10.1216/rmjm/1181069654
  • 5. I. Newton, Enumeratio linearum tertij ordinis, The Mathematical Papers of Isaac Newton. Vol. 7, Cambridge Univ. Press, Cambridge, 1976, pp. 565-645.

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Additional Information

A. B. Korchagin
Affiliation: Department of Radiophysics, Lobachevsky State University, Gagarin Ave. 23, Nizhniǐ Novgorod 603950, Russia
Email: akorchag@yandex.ru

DOI: http://dx.doi.org/10.1090/S1061-0022-2013-01268-4
Keywords: Isotopy and affine classification of cubics
Received by editor(s): October 5, 2011
Published electronically: July 24, 2013
Article copyright: © Copyright 2013 American Mathematical Society