Vector bundles on Olsson fans
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915777863483392 |
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| author | Battistella, Luca Carocci, Francesca Wise, Jonathan |
| author_facet | Battistella, Luca Carocci, Francesca Wise, Jonathan |
| contents | Artin fans are algebro-geometric incarnations of cone complexes. We study weakly convex Olsson fans, generalising Artin fans in two ways: first, they admit lineality spaces, thus including tropical tori as well; second, they are defined over a base logarithmic scheme, thus providing a relative version of equivariant toric geometries. We determine conditions under which Olsson fans are well-behaved, in the sense that their geometry is determined combinatorially. We undertake the study of quasicoherent sheaves, and in particular vector bundles, on Olsson fans: we describe their moduli stack in the case of a (subdivided) cone, and some failures of algebraicity in the general case; Weyl convexity shows up naturally in this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_05685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Vector bundles on Olsson fans Battistella, Luca Carocci, Francesca Wise, Jonathan Algebraic Geometry 14T99, 14M25, 14A20, 14D20 Artin fans are algebro-geometric incarnations of cone complexes. We study weakly convex Olsson fans, generalising Artin fans in two ways: first, they admit lineality spaces, thus including tropical tori as well; second, they are defined over a base logarithmic scheme, thus providing a relative version of equivariant toric geometries. We determine conditions under which Olsson fans are well-behaved, in the sense that their geometry is determined combinatorially. We undertake the study of quasicoherent sheaves, and in particular vector bundles, on Olsson fans: we describe their moduli stack in the case of a (subdivided) cone, and some failures of algebraicity in the general case; Weyl convexity shows up naturally in this context. |
| title | Vector bundles on Olsson fans |
| topic | Algebraic Geometry 14T99, 14M25, 14A20, 14D20 |
| url | https://arxiv.org/abs/2602.05685 |