We suggest an effective algorithm for the first Bertini theorem in the case of the ground field of nonzero characteristic. This allows us to improve the double exponential lower bound for the degree of any system of generators of a polynomial ideal over a ground field. Bibliography: 5 titles.
Similar content being viewed by others
References
A. L. Chistov, “Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time,” Zap. Nauch. 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 bound for the degree of a system of equations giving the variety of reducible polynomials,” Algebra Analiz, 24, No. 3, 199–222 (2012).
A. L. Chistov, “An improvement of the complexity bound for solving system of polynomial equations,” Zap. Nauchn. Semin. POMI, 390, 299–306 (2011).
A. L. Chistov, “A deterministic polynomial-time algorithm for 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
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 403, 2012, pp. 172–196.
Rights and permissions
About this article
Cite this article
Chistov, A.L. An effective version of the first Bertini theorem in nonzero characteristic and its applications. J Math Sci 190, 503–514 (2013). https://doi.org/10.1007/s10958-013-1267-z
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-013-1267-z