Gröbner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915191091888128 |
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| author | Şen, Büşra Karadeniz |
| author_facet | Şen, Büşra Karadeniz |
| contents | 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 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_08118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gröbner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities Şen, Büşra Karadeniz Algebraic Geometry 14B05, 14M25, 32S45 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 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. |
| title | Gröbner Fans and Minimal Embedded Toric Resolutions of Rational Double Point Singularities |
| topic | Algebraic Geometry 14B05, 14M25, 32S45 |
| url | https://arxiv.org/abs/2503.08118 |