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arXiv · 2507.23259

Notes on the cohomology of partial Hessenberg varieties

Tatsuya Horiguchi·Mikiya Masuda·Takashi Sato·Haozhi Zeng
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Abstract

Hessenberg varieties are a family of subvarieties of full flag varieties. This family contains well-known varieties such as Springer fibers, Peterson varieties, and permutohedral varieties. It was introduced by De Mari-Procesi-Shayman in 1992 and has been actively studied in this decade. In particular, unexpected relations to hyperplane arrangements and the Stanley-Stembridge conjecture in graph theory have been discovered. Hessenberg varieties can be defined in partial flag varieties. In this paper, we study their cohomology by relating them to the cohomology of Hessenberg varieties in the full flag varieties.

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Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato, Haozhi Zeng. 2025-07-31. Notes on the cohomology of partial Hessenberg varieties. https://arxiv.org/abs/2507.23259

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