[Author]
A. L. Chistov
[Title]
Efficient construction of local parameters of irreducible
components of an algebraic variety in nonzero characteristic
[AMS Subj-class]
14Q15 Higher-dimensional varieties
[Abstract]
Consider an $(n-s)$-dimensional algebraic variety $W$ defined over an
infinite field $k$ of nonzero characteristic $p$ and irreducible over this
field. Let $W$ be a subvariety of the projective space of dimension $n$. We
prove that the local ring of $W$ has a sequence of local parameters
represented by $s$ non--homogeneous polynomials with the product of degrees
less than the degree of the variety multiplied to a constant depending on
$n$. This allows to prove the existence of effective smooth cover and smooth
stratification of an algebraic variety in the case of ground field of
nonzero characteristic. The paper extends the analogous results of the author
obtained earlier from zero to nonzero characteristic of the ground field.
[Comments]
LaTeX, English, 23 pp.
[Contact e-mail]
sliss@iias.spb.su