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

Let V be a projective algebraic variety of degree D and dimension n nonsingular in codimension one. Then the construction of the normalization of V can be canonically reduced, within time polynomial in the size of the input and Dn0(1), to solving a linear equation aX + bY + cZ = 0 over a polynomial ring. We describe a plan of proving this result with all lemmas. Bibliography: 4 titles. © 2010 Springer Science+Business Media, Inc.