Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings

Jyoti Dasgupta; Chandranandan Gangopadhyay; Kiumars Kaveh; Christopher Manon

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arXiv · 2406.02912

Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings

Jyoti Dasgupta·Chandranandan Gangopadhyay·Kiumars Kaveh·Christopher Manon

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Abstract

We give a combinatorial classification of torus equivariant vector bundles on a (normal) projective T-variety of complexity-one. This extends the classification of equivariant line bundles on complexity-one T-varieties by Petersen-S\"uss on one hand, and Klyachko's classification of equivariant vector bundles on toric varieties on the other hand. A main ingredient in our classification is the classification of torus equivariant vector bundles on toric schemes over a DVR in terms of piecewise affine maps to the (extended) Bruhat-Tits building of the general linear group.

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Jyoti Dasgupta, Chandranandan Gangopadhyay, Kiumars Kaveh, Christopher Manon. 2024-06-05. Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings. https://arxiv.org/abs/2406.02912

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