Classification of homogeneous locally nilpotent derivations of \(k[x,y,z]\). I: Positive gradings of positive type (Q882635)

Let \({k}\) be a field of characteristic zero, let \(a,b,c\) be relatively prime positive integers, and define a grading ``\(g\)'' on the polynomial ring \(B = {k}[X,Y,Z]\) by declaring that \(X, Y,Z\) are homogeneous of degrees \(a, b, c\), respctively. The author of this paper considers the problem of classifying \({g}\)-homogeneous locally nilpotent derivations of \(B\). He solves the case where \({g}\) has positive type, which means that \(a, b, c\) are not pairwise relatively prime. The case where \(a, b, c\) are pairwise relatively prime is solved in a subsequent paper by the author.