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arXiv · 2003.12286

Fano and weak Fano Hessenberg varieties

Hiraku Abe·Naoki Fujita·Haozhi Zeng
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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 anti-canonical 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. 2020-03-27. Fano and weak Fano Hessenberg varieties. https://arxiv.org/abs/2003.12286

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