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Journal of Mathematical Sciences

, Volume 168, Issue 3, pp 478–490 | Cite as

An overview of effective normalization of a projective algebraic variety nonsingular in codimension one

  • A. L. Chistov
Article
  • 26 Downloads

Let V be a projective algebraic variety of degree D and dimension n nonsingular in codimension one. Then the construction of the normalization of V can be canonically reduced, within time polynomial in the size of the input and \( {D^{{n^{O(1)}}}} \), to solving a linear equation aX + bY + cZ = 0 over a polynomial ring. We describe a plan of proving this result with all lemmas. Bibliography: 4 titles.

Keywords

Russia Linear Equation General Position Algebraic Variety Polynomial Ring 
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References

  1. 1.
    A. L. Chistov, "Polynomial complexity of the Newton—Puiseux algorithm,” Lect. Notes Comput. Sci., 233, 247–255 (1986).CrossRefMathSciNetGoogle Scholar
  2. 2.
    A. L. Chistov, “Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time,” Zap. Nauchn. Semin. LOMI, 137, 124–188 (1984).MATHMathSciNetGoogle Scholar
  3. 3.
    A. L. Chistov, “Double-exponential lower bound for the degree of a system of generators of a polynomial prime ideal,” Algebra Analiz, 20, No. 6, 186–213 (2008).Google Scholar
  4. 4.
    A. L. Chistov, “A deterministic polynomial-time algorithm tor the first Bertini theorem,” Preprint of the St. Petersburg Mathematical Society (2004), http://www.MathSoc.spb.ru.

Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia

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