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

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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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     author = {A. L. Chistov},
     title = {An overview of effective normalization of a~nonsingular in codimension one projective algebraic variety},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {295--317},
     publisher = {mathdoc},
     volume = {373},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2009_373_a18/}
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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/