Higher rank instantons sheaves on Fano threefolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909584157835264 |
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| author | Comaschi, Gaia Faenzi, Daniele |
| author_facet | Comaschi, Gaia Faenzi, Daniele |
| contents | We define instanton sheaves of higher rank on smooth Fano threefolds X of Picard rank one and show that their topological classification depends on two integers, namely the rank n (or the half of it, if the Fano index of X is odd) and the charge k. We elucidate the value of the minimal charge k0 of slope-stable n-instanton bundles (except for Fano threefolds of index 1 and genus 3 or 4), as an integer depending only on the genus of X and on n and we prove the existence of slope-stable n-instanton bundles of charge k greater than k0. Next, we study the acyclic extension of instantons on Fano threefolds with curvilinear Kuznetsov component and give a monadic description when the intermediate Jacobian is trivial. Finally, we provide several features of a general element in the main component of the moduli space of intantons, such as and generic splitting over rational curves contained in X and stable restriction to a K3 section S of X, and give applications to Lagrangian subvarieties of moduli spaces of sheaves on S. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_13505 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Higher rank instantons sheaves on Fano threefolds Comaschi, Gaia Faenzi, Daniele Algebraic Geometry We define instanton sheaves of higher rank on smooth Fano threefolds X of Picard rank one and show that their topological classification depends on two integers, namely the rank n (or the half of it, if the Fano index of X is odd) and the charge k. We elucidate the value of the minimal charge k0 of slope-stable n-instanton bundles (except for Fano threefolds of index 1 and genus 3 or 4), as an integer depending only on the genus of X and on n and we prove the existence of slope-stable n-instanton bundles of charge k greater than k0. Next, we study the acyclic extension of instantons on Fano threefolds with curvilinear Kuznetsov component and give a monadic description when the intermediate Jacobian is trivial. Finally, we provide several features of a general element in the main component of the moduli space of intantons, such as and generic splitting over rational curves contained in X and stable restriction to a K3 section S of X, and give applications to Lagrangian subvarieties of moduli spaces of sheaves on S. |
| title | Higher rank instantons sheaves on Fano threefolds |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.13505 |