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Zapiski Nauchnykh Seminarov POMI, 2014, Volume 421, Pages 214–249
(Mi znsl5759)
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This article is cited in 1 scientific paper (total in 1 paper)
A deterministic polynomial-time algorithm for the first Bertini theorem. II
A. L. Chistov St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
Abstract:
Consider a projective algebraic variety $W$ which is an irreducible component of a set of all common zeroes of a family of homogeneous polynomials of degrees 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. This algorithm is deterministic and polynomial in $(dd')^n$ and the size of input. This paper is the second in the tree-part series.
Key words and phrases:
the first Bertini theorem, polynomial algorithm.
Received: 12.11.2013
Citation:
A. L. Chistov, “A deterministic polynomial-time algorithm for the first Bertini theorem. II”, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Zap. Nauchn. Sem. POMI, 421, POMI, St. Petersburg, 2014, 214–249; J. Math. Sci. (N. Y.), 200:6 (2014), 769–784
Linking options:
https://www.mathnet.ru/eng/znsl5759 https://www.mathnet.ru/eng/znsl/v421/p214
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Abstract page: | 244 | Full-text PDF : | 48 | References: | 42 |
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