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arXiv · 2503.08118

Gr\"obner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities

Büşra Karadeniz Şen
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Abstract

In [19], the authors give minimal embedded toric resolutions of ADE-singularities in C^3 by constructing regular refinements of their dual Newton polyhedrons with the elements of their embedded valuation sets derived from the jet schemes constructed in [18]. On the other hand in [1] and [2], the authors represent the Gr\"obner fan of a Newton non-degenerate variety and prove that a regular refinement of the Gr\"obner fan of such a singularity yields an embedded toric resolution. In this paper, we reconstruct embedded toric resolutions of ADE-singularities: We give the explicit constructions of their Gr\"obner fans and refine them using the concept of profile.

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Büşra Karadeniz Şen. 2025-03-11. Gr\"obner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities. https://arxiv.org/abs/2503.08118

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