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Efficient construction of local parameters for irreducible components of an algebraic variety in nonzero characteristic

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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 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 an effective smooth cover and a smooth stratification of an algebraic variety in the case of the ground field of nonzero characteristic, extending the analogous results of the author obtained earlier for the ground field of zero characteristic. Bibliography: 6 titles.

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References

  1. A. L. Chistov, “Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time,” Zap. Nauchn. Semin. LOMI, 137, 124–188 (1984).

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  2. A. L. Chistov, “Efficient construction of local parameters of irreducible components of an algebraic variety,” Tr. St.Peterbg. Mat. Obshch., 7, 230–266 (1999).

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  3. A. L. Chistov, “Efficient smooth stratification of an algebraic variety in zero characteristic and its applications,” Zap. Nauchn. Semin. POMI, 266, 254–311 (2000).

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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 Math. Soc., #13 (2004), http://www.mathsoc.spb.ru/preprint/2004/index.html#13.

  5. A. L. Chistov, “Polynomial time computation of the degrees of algebraic varieties in zero characteristic and its applications,” Zap. Nauchn. Semin. POMI, 258, 7–59 (1999).

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  6. I. R. Shafarevich, Basic Algebraic Geometry, Springer-Verlag, New York (1972).

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Authors and Affiliations

  1. St. Petersburg Department of the Steklov Mathematical Institute, St.Petersburg, Russia

    A. L. Chistov

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  1. A. L. Chistov
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Additional information

To A. M. Vershik with sincere gratitude and respect

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 326, 2005, pp. 248–278.

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Chistov, A.L. Efficient construction of local parameters for irreducible components of an algebraic variety in nonzero characteristic. J Math Sci 140, 480–496 (2007). https://doi.org/10.1007/s10958-007-0455-0

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  • DOI: https://doi.org/10.1007/s10958-007-0455-0

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