TY - JOUR
T1 - Equivariant Vector Bundles on Complexity-One T-Varieties and Bruhat–Tits Buildings
AU - Dasgupta, Jyoti
AU - Gangopadhyay, Chandranandan
AU - Kaveh, Kiumars
AU - Manon, Christopher
N1 - Publisher Copyright:
© The Author(s) 2025. Published by Oxford University Press. All rights reserved.
PY - 2025/5/1
Y1 - 2025/5/1
N2 - 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–Süß 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.
AB - 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–Süß 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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U2 - 10.1093/imrn/rnaf124
DO - 10.1093/imrn/rnaf124
M3 - Article
AN - SCOPUS:105006521501
SN - 1073-7928
VL - 2025
JO - International Mathematics Research Notices
JF - International Mathematics Research Notices
IS - 10
M1 - rnaf124
ER -