6 citations · 18 across the 12 of their papers we have counts for
13 papers
Totally nonnegative Peterson variety and strongly dominant weight polytope
Hiraku Abe, Tao Gui, Haozhi Zeng
We study the totally nonnegative part of the Peterson variety in arbitrary Lie type and establish its connection to the strongly dominant weight polytope. In particular, we prove t…
Notes on the cohomology of partial Hessenberg varieties
Tatsuya Horiguchi, Mikiya Masuda, Takashi Sato +1
Hessenberg varieties are a family of subvarieties of full flag varieties. This family contains well-known varieties such as Springer fibers, Peterson varieties, and permutohedral v…
Automorphisms of GKM graphs and regular semisimple Hessenberg varieties
Donghoon Jang, Shintarô Kuroki, Mikiya Masuda +2
A regular semisimple Hessenberg variety is a smooth subvariety of the full flag variety associated with a regular semisimple matrix…
Totally nonnegative part of the Peterson variety in Lie type A
Hiraku Abe, Haozhi Zeng
The Peterson variety (which we denote by ) is a subvariety of the flag variety, introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag vari…
Peterson varieties and toric orbifolds associated to Cartan matrices
Hiraku Abe, Haozhi Zeng
The Peterson variety is a remarkable variety introduced by Dale Peterson to describe the quantum cohomology rings of all the partial flag varieties. The rational cohomology ring of…
Equivariant cohomology ring of open torus manifolds with locally standard actions
Yueshan Xiong, Haozhi Zeng
The notation of torus manifolds were introduced by A. Hattori and M. Masuda. Toric manifolds, quasitoric manifolds, topological toric manifolds, toric origami manifolds and -sym…
The integral cohomology rings of Peterson varieties in type A
Hiraku Abe, Haozhi Zeng
In this paper, we study the ring structure of the integral cohomology of the Peterson variety of type . We give two kinds of descriptions: (1) we show that it is is…
Geometry of Peterson Schubert calculus in type A and left-right diagrams
Hiraku Abe, Tatsuya Horiguchi, Hideya Kuwata +1
We introduce an additive basis of the integral cohomology ring of the Peterson variety which reflects the geometry of certain subvarieties of the Peterson variety. We explain the p…
Fano and weak Fano Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Regular semisimple Hessenberg varieties are smooth subvarieties of the flag variety, and their examples contain the flag variety itself and the permutohedral variety which is a tor…
Geometry of regular Hessenberg varieties
Hiraku Abe, Naoki Fujita, Haozhi Zeng
Let be a complex semisimple Lie algebra. For a regular element in and a Hessenberg space , we consider a regular Hessenbe…
Torsion in the cohomology of torus orbifolds
Hideya Kuwata, Mikiya Masuda, Haozhi Zeng
We study torsion in the integral cohomology of a certain family of -dimensional orbifolds with actions of the -dimensional compact torus. Compact simplicial toric variet…
Toric origami structures on quasitoric manifolds
Anton Ayzenberg, Mikiya Masuda, Seonjeong Park +1
We construct quasitoric manifolds of dimension 6 and higher which are not equivariantly homeomorphic to any toric origami manifold. All necessary topological definitions and combin…
Cohomology of toric origami manifolds with acyclic proper faces
Anton Ayzenberg, Mikiya Masuda, Seonjeong Park +1
A toric origami manifold is a generalization of a symplectic toric manifold (or a toric symplectic manifold). The origami symplectic form is allowed to degenerate in a good control…