Gr\"obner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities
Algebraic Geometry
2025-03-12 v1
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.
Keywords
Cite
@article{arxiv.2503.08118,
title = {Gr\"obner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities},
author = {Büşra Karadeniz Şen},
journal= {arXiv preprint arXiv:2503.08118},
year = {2025}
}