Stability of syzygy bundles on varieties of Picard number one
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908382246469632 |
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| author | Jiang, Chen Ren, Peng |
| author_facet | Jiang, Chen Ren, Peng |
| contents | We give a criterion for slope-stability of the syzygy bundle of a globally generated ample line bundle on a smooth projective variety of Picard number $1$ in terms of Hilbert polynomial. As applications, we prove the stability of syzygy bundles on many varieties, such as smooth Fano or Calabi--Yau complete intersections, hyperkähler varieties of Picard number 1, abelian varieties of Picard number $1$, rational homogeneous varieties of Picard number 1, weak Calabi--Yau varieties of Picard number $1$ of dimension $\leq 4$, and Fano varieties of Picard number $1$ of dimension $\leq5$. Also we prove the stability of syzygy bundles on all hyperkähler varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_00476 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stability of syzygy bundles on varieties of Picard number one Jiang, Chen Ren, Peng Algebraic Geometry 14H60 (Primary) 14C20, 14M10, 14J45, 14J42, 14J32, 14M17 (Secondary) We give a criterion for slope-stability of the syzygy bundle of a globally generated ample line bundle on a smooth projective variety of Picard number $1$ in terms of Hilbert polynomial. As applications, we prove the stability of syzygy bundles on many varieties, such as smooth Fano or Calabi--Yau complete intersections, hyperkähler varieties of Picard number 1, abelian varieties of Picard number $1$, rational homogeneous varieties of Picard number 1, weak Calabi--Yau varieties of Picard number $1$ of dimension $\leq 4$, and Fano varieties of Picard number $1$ of dimension $\leq5$. Also we prove the stability of syzygy bundles on all hyperkähler varieties. |
| title | Stability of syzygy bundles on varieties of Picard number one |
| topic | Algebraic Geometry 14H60 (Primary) 14C20, 14M10, 14J45, 14J42, 14J32, 14M17 (Secondary) |
| url | https://arxiv.org/abs/2412.00476 |