A BOUND FOR THE MILNOR SUM OF PROJECTIVE PLANE CURVES IN TERMS OF GIT

Title & Authors
A BOUND FOR THE MILNOR SUM OF PROJECTIVE PLANE CURVES IN TERMS OF GIT
Shin, Jaesun;

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 than or equal to $\small{(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $\small{(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}}$ 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.
Keywords
Milnor sum;polar degree;GIT;
Language
English
Cited by
References
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