An overview of effective normalization of a nonsingular in codimension one projective algebraic variety

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.