Geodesic
Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 248-278 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $s$ nonhomogeneous polynomials with the product of degrees less than the degree of the variety multiplied by a constant depending on $n$. This allows us 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 in the case of zero characteristic of the ground field. 
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     title = {Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic},
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A. L. Chistov. Efficient construction of local parameters of irreducible components of an algebraic variety in nonzero characteristic. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIII, Tome 326 (2005), pp. 248-278. http://geodesic.mathdoc.fr/item/ZNSL_2005_326_a13/

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[4] A. L. Chistov, A correction in the statement of my theorem on the efficient smooth cover and smooth stratification of an algebraic variety, Preprint of the St.-Petersburg Mathematical Society, No 13, 2004; http://www.mathsoc.spb.ru/preprint/2004/index.html#13

[5] A. L. Chistov, “Vychislenie stepenei algebraicheskikh mnogoobrazii nad polem nulevoi kharakteristiki za polinomialnoe vremya i ego prilozheniya”, Zap. nauchn. semin. POMI, 258, 1999, 7–59 | MR | Zbl

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