[Authors]
 A. L. Chistov

[Title]
 A deterministic polynomial--time algorithm for the first Bertini theorem

[AMS Subj-class]
 14Q15 Higher-dimensional varieties

[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.

[Comments]
 LaTeX, English, 71 pp.

[Contact e-mail]
 sliss@iias.spb.su