Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.06779 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866929712664674304 |
|---|---|
| author | Veselov, A. P. |
| author_facet | Veselov, A. P. |
| contents | We show that the Markov fractions introduced recently by Boris Springborn are precisely the slopes of the exceptional vector bundles on $\mathbb P^2$ studied in 1980s by Drèzet and Le Potier and by Rudakov. In particular, we provide a simpler proof of Rudakov's result claiming that the ranks of the exceptional bundles on $\mathbb P^2$ are Markov numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_06779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ Veselov, A. P. Number Theory Algebraic Geometry 11H99, 14J60 We show that the Markov fractions introduced recently by Boris Springborn are precisely the slopes of the exceptional vector bundles on $\mathbb P^2$ studied in 1980s by Drèzet and Le Potier and by Rudakov. In particular, we provide a simpler proof of Rudakov's result claiming that the ranks of the exceptional bundles on $\mathbb P^2$ are Markov numbers. |
| title | Markov fractions and the slopes of the exceptional bundles on $\mathbb P^2$ |
| topic | Number Theory Algebraic Geometry 11H99, 14J60 |
| url | https://arxiv.org/abs/2501.06779 |