Toric principal bundles, piecewise linear maps and Tits buildings
Kiumars Kaveh, Christopher Manon

TL;DR
This paper introduces a new classification framework for toric principal bundles using piecewise linear maps to Tits buildings, extending Klyachko's work and applying to various algebraic groups.
Contribution
It defines piecewise linear maps to Tits buildings and shows they classify toric principal G-bundles, generalizing existing classifications for vector bundles.
Findings
Classifies toric principal G-bundles via piecewise linear maps
Recovers Klyachko's classification of toric vector bundles
Provides new classifications for orthogonal and symplectic toric bundles
Abstract
We define the notion of a piecewise linear map from a fan to , the cone over the Tits building of a linear algebraic group . Let be a toric variety with fan . We show that when is reductive the set of integral piecewise linear maps from to classifies the isomorphism classes of (framed) toric principal -bundles on . This in particular recovers Klyachko's classification of toric vector bundles, and gives new classification results for the orthogonal and symplectic toric principal bundles.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology
