On a Computational Approach to the Nash Blowup Problem Article Swipe
Castillo, Federico
,
Duarte, Daniel
,
Leyton-Álvarez, Maximiliano
,
Liendo, Alvaro
·
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2511.17862
YOU?
·
· 2025
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2511.17862
In this paper we describe the implementation that led to the counterexamples to the Nash blowup conjectures recently discovered by the authors. We also provide new examples of toric varieties with prescribed singularities that are not resolved by the normalized Nash blowup, including cyclic quotient singularities, toric hypersurfaces, and Q-factorial Gorenstein singularities. In addition, we report extensive computational evidence: tens of thousands of two-dimensional toric varieties that are resolved by iterating the Nash blowup, and millions of three-dimensional toric varieties that are resolved by iterating the normalized Nash blowup. This provides positive evidence for the remaining open cases of the conjectures.
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- preprint
- Landing Page
- https://doi.org/10.48550/arxiv.2511.17862
- OA Status
- green
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https://doi.org/10.48550/arxiv.2511.17862Digital Object Identifier
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On a Computational Approach to the Nash Blowup ProblemWork title
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preprintOpenAlex work type
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2025Year of publication
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2025-11-22Full publication date if available
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Castillo, Federico, Duarte, Daniel, Leyton-Álvarez, Maximiliano, Liendo, AlvaroList of authors in order
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https://doi.org/10.48550/arxiv.2511.17862Publisher landing page
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YesWhether a free full text is available
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greenOpen access status per OpenAlex
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https://doi.org/10.48550/arxiv.2511.17862Direct OA link when available
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Mathematics, Counterexample, Nash equilibrium, Quotient, Gravitational singularity, Toric variety, Applied mathematics, Computer science, Computational complexity theory, AlgorithmTop concepts (fields/topics) attached by OpenAlex
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0Total citation count in OpenAlex
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