Title: A BOUND FOR THE MILNOR SUM OF PROJECTIVE PLANE CURVES IN TERMS OF GIT
Abstract:Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less t...Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. P loski proved that the Milnor number of an isolated singlar point of C is less than or equal to <TEX>$(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$</TEX>. In this paper, we prove that the Milnor sum of C is also less than or equal to <TEX>$(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$</TEX> and the equality holds if and only if C is a P loski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.Read More