Toric principal bundles, piecewise linear maps and Tits buildings

Kiumars Kaveh; Christopher Manon

doi:10.1007/s00209-022-03094-5

Toric principal bundles, piecewise linear maps and Tits buildings

Kiumars Kaveh, Christopher Manon

Mathematics

Research output: Contribution to journal › Article › peer-review

5 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 X_Σ 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 X_Σ. 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 language	English
Pages (from-to)	1367-1392
Number of pages	26
Journal	Mathematische Zeitschrift
Volume	302
Issue number	3
DOIs	https://doi.org/10.1007/s00209-022-03094-5
State	Published - Nov 2022

Bibliographical note

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

Funding

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)

Funders	Funder number
Simons Collaboration	714052, 587209, DMS-1500966, DMS-2101911
National Science Foundation Arctic Social Science Program	DMS-1601303, 1500966, DMS-2101843

ASJC Scopus subject areas

General Mathematics

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Cite this

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Toric principal bundles, piecewise linear maps and Tits buildings

Abstract

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