Hyperplane arrangements and Hessenberg varieties
speaker: Takuro Abe (Kyoto University)abstract: Hessenberg varieties were introduced by De Mari, Procesi and Shayman as a generalization of flag varieties. Recently, for the regular nilpotent and regular semisimple cases, their topologies are intensively studied, and related to combinatorial and (geometric) representational aspects. However, the algebraic structure of their cohomology groups have been unknown except for the case of type A. Recalling the fact that their cohomology rings are isomorphic to the coinvariant algebras, and Kyoji Saito's original proof of the freeness of Weyl arrangements by using basic invariants, we give a presentation of the cohomology group of a regular nilpotent Hessenberg variety by using a logarithmic derivation module of certain hyperplane arrangements (ideal arrangements) coming from the Hessenberg variety. Also, several properties of cohomology groups like complete intersection, hard Lefschetz properties and Hodge-Riemann relations are shown.Karim
timetable:
Wed 7 Jun, 9:00 - 9:40, Aula Dini
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