A deterministic polynomial-time algorithm for the first Bertini theorem.~II
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 214-249
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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.
@article{ZNSL_2014_421_a14,
author = {A. L. Chistov},
title = {A deterministic polynomial-time algorithm for the first {Bertini} {theorem.~II}},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {214--249},
publisher = {mathdoc},
volume = {421},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a14/}
}
A. L. Chistov. A deterministic polynomial-time algorithm for the first Bertini theorem.~II. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXIII, Tome 421 (2014), pp. 214-249. http://geodesic.mathdoc.fr/item/ZNSL_2014_421_a14/