Geodesic
An overview of effective normalization of a nonsingular in codimension one projective algebraic variety
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 295-317 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $V$ be a nonsingular in codimension one projective algebraic variety of degree $D$ and of dimension $n$. Then the construction of the normalization of $V$ can be reduced canonically within the time polynomial in the size of the input and $D^{n^{O(1)}}$ to solving a linear equation $aX+bY+cZ=0$ over a polynomial ring. We describe a plan with all lemmas to prove this result. Bibl. – 4 titles. 
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A. L. Chistov. An overview of effective normalization of a nonsingular in codimension one projective algebraic variety. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XVII, Tome 373 (2009), pp. 295-317. http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a18/

[1] A. L. Chistov, “Polynomial complexity of the Newton–Puiseux algorithm”, Lecture Notes in Computer Science, 233, Springer, New York–Berlin–Heidelberg, 1986, 247–255 | DOI | MR

[2] A. L. Chistov, “Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time”, Zap. Nauchn. Semin. LOMI, 137, 1984, 124–188 | MR | Zbl

[3] A. L. Chistov, “Double-exponential lower bound for the degree of a system of generators of a polynomial prime ideal”, Algebra Analiz, 20:6 (2008), 186–213 | MR

[4] A. L. Chistov, A deterministic polynomial-time algorithm for the first Bertini theorem, Preprint, St. Petersburg Mathematical Society, 2004; http://www.MathSoc.spb.ru