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arxiv:2301.03762
Regular semisimple Hessenberg varieties with cohomology rings generated in degree two
Published on Nov 9, 2025
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Abstract
A regular semisimple Hessenberg variety Hess(S,h) is a smooth subvariety of the flag variety determined by a square matrix S with distinct eigenvalues and a Hessenberg function h. The cohomology ring H^*(Hess(S,h)) is independent of the choice of S and is not explicitly described except for a few cases. In this paper, we characterize the Hessenberg function h such that H^*(Hess(S,h)) is generated in degree two as a ring. It turns out that such h is what is called a (double) lollipop.
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