On the T-equivariant cohomology of Hessenberg varieties

2022/02/04 by Argáez, Daniel Sánchez, Zaldívar, Felipe
#14M12 #14M15 #14N15 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.02346

Abstract

For an endomorphism s:V→ V of a finite dimensional complex vector space and an action of a torus T on the full flag variety GL_n(\mathbb C)/B, we give a description of its fixed point set when s is semisimple or regular nilpotent. We also compute the one dimensional orbits of this action on the Hessenberg subvariety Hes(s,h)⊆ GL_n(\mathbb C)/B for any Hessenberg function h. For the action of the one dimensional torus S and a regular nilpotent endomorphism N:V→ V, we give a new computation of the equivariant cohomology of the Hessenberg variety Hes(N,h) for any Hessenberg function using determinantal conditions.

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