Poisson slices and Hessenberg varieties

Abstract: Hessenberg varieties constitute a rich and well-studied class of closed subvarieties in the flag variety. Prominent examples include Grothendieck-Springer fibres, the Peterson variety, and the projective toric variety associated to the Weyl chambers. These last two examples belong to the family of standard Hessenberg varieties, whose total space is known to be a log symplectic variety. I will exhibit this total space as a Poisson slice in the log cotangent bundle of the wonderful compactification, thereby building on Balibanu's recent results. This will yield a canonical closed embedding of each standard Hessenberg variety into the wonderful compactification.

This represents joint work with Markus Röser.

algebraic geometry

Audience: researchers in the topic

UC Davis algebraic geometry seminar