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Gröbner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities

2025/03/11 by Şen, Büşra Karadeniz
#14B05 #14M25 #32S45 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.08118

Abstract

In [19], the authors give minimal embedded toric resolutions of ADE-singularities in C3 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 Gröbner fan of a Newton non-degenerate variety and prove that a regular refinement of the Gröbner 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 Gröbner fans and refine them using the concept of profile.

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