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arXiv · 1907.06281

Multiplier ideals of analytically irreducible plane curves

Mingyi Zhang
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Abstract

Let $S$ be a Puiseux series of the germ of an analytically irreducible plane curve $Z$. We provide a new perspective to construct a set of polynomials $F=\{F_1,\ldots, F_{g-1}\}$ associated to $S$, which is a special choice of maximal contact elements constructed in [AMB17] and approximate roots defined in [Dur18], [AM73a], [AM73b]. Using these polynomials as building blocks, we describe a set of generators of multiplier ideals of the form $\mathfrak{I}(αZ)$ with $0<α<1$ a rational number, which recovers the results about irreducible plane curves in [AMB17], [Dur18].

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Mingyi Zhang. 2019-09-30. Multiplier ideals of analytically irreducible plane curves. https://arxiv.org/abs/1907.06281

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