Monotonic invariants under blowups

Zhenjian Wang

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arXiv · 1904.08588

Monotonic invariants under blowups

Zhenjian Wang

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Abstract

We prove that the numerical invariant $3\mu-4\tau$ of a reduced irreducible plane curve singularity germ is non-negative, non-decreasing under blowups and strictly increasing unless the curve is non-singular. This provides a new perspective to understand the question posed by A. Dimca and G.-M. Greuel. Moreover, our work can be put in the general framework of discovering monotonic invariants under blowups.

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Zhenjian Wang. 2019-04-18. Monotonic invariants under blowups. https://arxiv.org/abs/1904.08588

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