Toric principal bundles, piecewise linear maps and Tits buildings

Kiumars Kaveh, Christopher Manon

Research output: Contribution to journalArticlepeer-review

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
JournalMathematische Zeitschrift
DOIs
StateAccepted/In press - 2022

Bibliographical note

Funding Information:
Kiumars Kaveh is partially supported by National Science Foundation Grants (DMS-1601303 and DMS-2101843) and a Simons Collaboration Grant (award number 714052). Also Christopher Manon is partially supported by National Science Foundation Grants (DMS-1500966 ans DMS-2101911) and a Simons Collaboration Grant (award number 587209)

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

ASJC Scopus subject areas

  • Mathematics (all)

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