[Authors]
 A. L. Chistov

[Title]
 Polynomial--time computation of the degree of a dominant morphism
 in zero--characteristic I

[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. We show how
 to compute the degree of a dominant rational morphism from $W$ to $W'$. The
 morphism is given by homogeneous polynomials of degree $d'$.  This algorithms
 is deterministic and polynomial in $(dd')^n$ and the size of input.

[Comments]
 LaTeX, English, 32 pp.
 Published in Russian:
 Chistov A. L.: ``Polynomial--time computation of the degree of a dominant
 morphism in zero--characteristic I'', Zap. Nauchn. Semin. St-Petersburg.
 Otdel. Mat.  Inst. Steklov (POMI) 307 (2004) p. 189--235.

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