A bound for the Milnor sum of projective plane curves in terms of GIT

2015/02/25 by Jae‐Sun Shin, Shin, Jaesun · 1 citation
Mathematics · Computer Science · Social Sciences · #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #Communism, Protests, Social Movements

paper · pdf · doi:10.48550/arxiv.1502.07138

Abstract

Let C be a projective plane curve of degree d whose singularities are all isolated. Suppose C is not concurrent lines. Płoski proved that the Milnor number of an isolated singlar point of C is less than or equal to (d-1)²-\lfloor (d)/(2) \rfloor. In this paper, we prove that the Milnor sum of C is also less than or equal to (d-1)²-\lfloor (d)/(2) \rfloor and the equality holds if and only if C is a Płoski curve. Furthermore, we find a bound for the Milnor sum of projective plane curves in terms of GIT.

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