Shintarô Kuroki
YOU?
Author Swipe
View article: Classification of locally standard torus actions
Classification of locally standard torus actions Open
An action of a torus T on a manifold M is locally standard if, at each point, the stabilizer is a sub-torus and the non-zero isotropy weights are a basis to its weight lattice. The quotient M/T is then a manifold-with-corners, decorated by…
View article: Equivariant cohomology of odd-dimensional complex quadrics from a combinatorial point of view
Equivariant cohomology of odd-dimensional complex quadrics from a combinatorial point of view Open
This paper aims to determine the ring structure of the torus equivariant cohomology of odd-dimensional complex quadrics by computing the graph equivariant cohomology of their corresponding GKM graphs. We show that its graph equivariant coh…
View article: Equivariant cohomology of even-dimensional complex quadrics from a combinatorial point of view
Equivariant cohomology of even-dimensional complex quadrics from a combinatorial point of view Open
The purpose of this paper is to determine the ring structure of the graph equivariant cohomology of the GKM graph induced from the even-dimensional complex quadrics. We show that the graph equivariant cohomology is generated by two types o…
View article: Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph
Borel-Hirzebruch type formula for the graph equivariant cohomology of a projective bundle over a GKM-graph Open
In this paper, we introduce the GKM theoretical counterpart of the equivariant complex vector bundles as the "leg bundle". We also provide a definition for the projectivization of a leg bundle and prove the Borel-Hirzebruch type formula fo…
View article: GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology
GKM graph locally modeled by $T^{n}\times S^{1}$-action on $T^{*}\mathbb{C}^{n}$ and its graph equivariant cohomology Open
We introduce a class of labeled graphs (with legs) which contains two classes of GKM graphs of $4n$-dimensional manifolds with $T^{n}\times S^{1}$-actions, i.e., GKM graphs of the toric hyperK${\rm\ddot{a}}$hler manifolds and of the cotang…
View article: Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold
Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold Open
To a direct sum of holomorphic line bundles, we can associate two fibrations,\nwhose fibers are, respectively, the corresponding full flag manifold and the\ncorresponding projective space. Iterating these procedures gives, respectively,\na…
View article: Flag Bott manifolds of general Lie type and their equivariant cohomology rings
Flag Bott manifolds of general Lie type and their equivariant cohomology rings Open
In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate…
View article: Upper bounds for the dimension of tori acting on GKM manifolds
Upper bounds for the dimension of tori acting on GKM manifolds Open
The aim of this paper is to give an upper bound for the dimension of a torus\n$T$ which acts on a GKM manifold $M$ effectively. In order to do that, we\nintroduce a free abelian group of finite rank, denoted by\n$\\mathcal{A}(\\Gamma,\\alp…