Higher discriminants of vector bundles and Schur functors
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915213601669120 |
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| author | D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio |
| author_facet | D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio |
| contents | We prove some closed formulas for the logarithmic Chern character of a locally free sheaf. The argument used is representation-theoretic and we connect these formulas with the actions of some Casimir elements of $\mathfrak{sl}_r$.
As an application, we give a recipe to construct slope polystable modular bundles on hyper-Kähler manifolds from old ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher discriminants of vector bundles and Schur functors D'Andrea, Alessandro Fatighenti, Enrico Onorati, Claudio Algebraic Geometry Representation Theory 14J60, 16S30, 17B10, 14J42 We prove some closed formulas for the logarithmic Chern character of a locally free sheaf. The argument used is representation-theoretic and we connect these formulas with the actions of some Casimir elements of $\mathfrak{sl}_r$. As an application, we give a recipe to construct slope polystable modular bundles on hyper-Kähler manifolds from old ones. |
| title | Higher discriminants of vector bundles and Schur functors |
| topic | Algebraic Geometry Representation Theory 14J60, 16S30, 17B10, 14J42 |
| url | https://arxiv.org/abs/2503.15365 |