A one-step counterexample to the normalized Nash blowup conjecture
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917392371679232 |
|---|---|
| author | Liendo, Alvaro Palomino, Ana Julisa Rodríguez, Gonzalo |
| author_facet | Liendo, Alvaro Palomino, Ana Julisa Rodríguez, Gonzalo |
| contents | We construct an explicit normal singular affine toric variety X of dimension five over an algebraically closed field of characteristic three such that the normalized Nash blowup of X already contains an open affine subset isomorphic to X. Combined with previously known examples, this yields one-step counterexamples in every dimension greater than or equal to five and every characteristic. The characteristic-three case is the most delicate: the previously known counterexample in dimension four requires a two-step iteration of the normalized Nash blowup, and our example demonstrates that in dimension five and higher the minimal number of iterations needed to produce a loop is one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07519 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A one-step counterexample to the normalized Nash blowup conjecture Liendo, Alvaro Palomino, Ana Julisa Rodríguez, Gonzalo Algebraic Geometry 14B05, 14E15, 14M25 We construct an explicit normal singular affine toric variety X of dimension five over an algebraically closed field of characteristic three such that the normalized Nash blowup of X already contains an open affine subset isomorphic to X. Combined with previously known examples, this yields one-step counterexamples in every dimension greater than or equal to five and every characteristic. The characteristic-three case is the most delicate: the previously known counterexample in dimension four requires a two-step iteration of the normalized Nash blowup, and our example demonstrates that in dimension five and higher the minimal number of iterations needed to produce a loop is one. |
| title | A one-step counterexample to the normalized Nash blowup conjecture |
| topic | Algebraic Geometry 14B05, 14E15, 14M25 |
| url | https://arxiv.org/abs/2604.07519 |