[Authors]
 A. L. Chistov

[Title]
 Monodromy and irreducibility criteria with algorithmic applications
 in zero--characteristic

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

[Abstract]
 Consider a projective algebraic variety $V$ which is the set of all common
 zeroes of homogeneous polynomials of degrees less than $d$ in $n+1$ variables
 in zero--characteristic. We suggest an algorithm to decide whether two (or
 more) given points of $V$ belong to the same irreducible component of $V$.
 Besides that we show how to construct for each $s<n$ an $(s+1)$--dimensional
 plane in the projective space such that the intersection of every irreducible
 component of dimension $n-s$ of $V$ with the constructed plane is transversal
 and is an irreducible curve.  These algorithms are deterministic and
 polynomial in $d^n$ and the size of input.

[Comments]
 LaTeX, English, 17 pp.
 Published in Russian:
 Chistov A. L.: ``Monodromy and irreducibility criteria
 with algorithmic applications in zero--characteristic'',
 Zap. Nauchn. Semin. St-Petersburg.  Otdel. Mat.
 Inst. Steklov (POMI) 292 (2002) p. 130--152.

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