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arXiv · 2602.05685

Vector bundles on Olsson fans

Luca Battistella·Francesca Carocci·Jonathan Wise
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Abstract

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.

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Luca Battistella, Francesca Carocci, Jonathan Wise. 2026-02-05. Vector bundles on Olsson fans. https://arxiv.org/abs/2602.05685

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