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Zapiski Nauchnykh Seminarov POMI, 2013, Volume 411, Pages 191–239
(Mi znsl5640)
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This article is cited in 2 scientific papers (total in 2 papers)
A deterministic polynomial-time algorithm for the first Bertini theorem. I
A. L. Chistov St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, St. Petersburg, Russia
Abstract:
Consider a projective algebraic variety $W$ that is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degree less than $d$ in $n+1$ variables in zero characteristic. Consider a linear system on $W$ given by homogeneous polynomials of degree $d'$. Under the conditions of the first Bertini theorem for $W$ and this linear system, we show how to construct an irreducible divisor in general position from the statement of this theorem. The algorithm is deterministic and polynomial in $(dd')^n$ and the size of the input.
Key words and phrases:
first Bertini theorem, polynomial algorithm.
Received: 04.02.2013
Citation:
A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. I”, Representation theory, dynamical systems, combinatorial methods. Part XXII, Zap. Nauchn. Sem. POMI, 411, POMI, St. Petersburg, 2013, 191–239; J. Math. Sci. (N. Y.), 196:2 (2014), 223–243
Linking options:
https://www.mathnet.ru/eng/znsl5640 https://www.mathnet.ru/eng/znsl/v411/p191
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Abstract page: | 342 | Full-text PDF : | 70 | References: | 52 |
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