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

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.


Russia Linear Equation General Position Algebraic Variety Polynomial Ring 
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  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),

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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