Dicritical Divisors and Jacobian Problem

The dicritical divisor coming out of integrable holonomie in dynamical systems which belong to the domain of real analysis gets miraculously married to the jacobian problem of algebraic geometry. This is a godsend for making inroads into the fortress jacobian. It also provides a sharp tool for studying local functions on algebraic as well as analytical surfaces. Although the jacobian problem is restricted to zero characteristic, it is amazing that the dicriticals, born out of real analysis, throw light on the theory of local rings of prime characteristic. We owe the real and complex theory of
dicriticals to the pioneers like Artal, Cassou-Nogues, Eisenbud, Fourrier, Mattei, Moussu, Neumann, Norbury and Rudolph. .........(continue)