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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A. L. Chistov, "Polynomial complexity of the Newton—Puiseux algorithm,” Lect. Notes Comput. Sci., 233, 247–255 (1986).
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).
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).
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
Published in Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 295–317.
Rights and permissions
About this article
Cite this article
Chistov, A.L. An overview of effective normalization of a projective algebraic variety nonsingular in codimension one. J Math Sci 168, 478–490 (2010). https://doi.org/10.1007/s10958-010-0001-3
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-010-0001-3