Toric principal bundles, piecewise linear maps and Tits buildings

Kiumars Kaveh, Christopher Manon

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We define the notion of a piecewise linear map from a fan Σ to B~ (G) , the cone over the Tits building of a linear algebraic group G. Let XΣ be a toric variety with fan Σ. We show that when G is reductive the set of integral piecewise linear maps from Σ to B~ (G) classifies the isomorphism classes of (framed) toric principal G-bundles on XΣ. This in particular recovers Klyachko’s classification of toric vector bundles, and gives new classification results for the orthogonal and symplectic toric principal bundles.

Original languageEnglish
Pages (from-to)1367-1392
Number of pages26
JournalMathematische Zeitschrift
Volume302
Issue number3
DOIs
StatePublished - Nov 2022

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

  • General Mathematics

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