Dimensions of type $A$ Hessenberg varieties over a fixed sheet

Megumi Harada, Martha Precup, Colleen Robichaux

Hessenberg varieties $\mathcal{H}\mathrm{ess}(\mathsf{X},\mathbf{h})$ are subvarieties of the flag variety parameterized by a Hessenberg function $\mathbf{h}:[n]\to [n]$ and a ma…