Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings
Algebraic Geometry
2024-06-06 v1
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.
Keywords
Cite
@article{arxiv.2406.02912,
title = {Equivariant vector bundles on complexity-one T-varieties and Bruhat-Tits buildings},
author = {Jyoti Dasgupta and Chandranandan Gangopadhyay and Kiumars Kaveh and Christopher Manon},
journal= {arXiv preprint arXiv:2406.02912},
year = {2024}
}
Comments
29 pages, 1 figure. arXiv admin note: text overlap with arXiv:2402.18712