Chistov, Alexander L.

Efficient Construction of Local Parameters of Irreducible Components
of an Algebraic Variety.

Email: sliss@iias.spb.su

Primary MSC:14Q15

Abstract:

Consider an $n-s$--dimensional algebraic variety $V$ defined over a perfect
infinite field $k$ and irreducible over this field which is a subvariety of the
projective space of dimension $n$. We prove that the local ring of $V$ has a
regular sequence (respectively if characteristic $char (k)=0$ a sequence of
local parameters) represented by $s$ non--homogeneous polynomials the product of
degrees of which is less than the degree of the variety multiplied to a constant
depending on $n$. In the case when $V$ is an irreducible component of an
algebraic variety given by a system of homogeneous polynomial equations of
degrees less than $d$ over a field of zero--characteristic the degrees of all
these local parameters are less then $d$ multiplied to a constant depending on
$n$. These constants depending on $n$ are estimated.

Comment: To be published in the Proceedings of the St. Petersburg
Mathematical Society.