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2022 Fano and Weak Fano Hessenberg Varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Michigan Math. J. Advance Publication 1-45 (2022). DOI: 10.1307/mmj/20205971

Abstract

Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety, which is a toric variety. We give a complete classification of Fano and weak Fano regular semisimple Hessenberg varieties in type A in terms of combinatorics of Hessenberg functions. In particular, we show that if the anticanonical bundle of a regular semisimple Hessenberg variety is nef, then it is in fact nef and big.

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Hiraku Abe. Naoki Fujita. Haozhi Zeng. "Fano and Weak Fano Hessenberg Varieties." Michigan Math. J. Advance Publication 1 - 45, 2022. https://doi.org/10.1307/mmj/20205971

Information

Received: 21 August 2020; Revised: 22 March 2021; Published: 2022
First available in Project Euclid: 12 May 2022

Digital Object Identifier: 10.1307/mmj/20205971

Subjects:
Primary: 14M15
Secondary: 05E10 , 14J45

Rights: Copyright © 2022 The University of Michigan

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