Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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A BOUND FOR THE MILNOR SUM OF PROJECTIVE PLANE CURVES IN TERMS OF GIT

  • Received : 2015.03.10
  • Published : 2016.03.01
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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 $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$. In this paper, we prove that the Milnor sum of C is also less than or equal to $(d-1)^2-{\lfloor}\frac{d}{2}{\rfloor}$ 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.

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References

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