30 citations · 184 across the 67 of their papers we have counts for
9 papers · 1 filter
Conic divisorial ideals and non-commutative crepant resolutions of edge rings of complete multipartite graphs
Akihiro Higashitani, Koji Matsushita
The first goal of the present paper is to study the class groups of the edge rings of complete multipartite graphs, denoted by , where $1 \leq r_1 \leq \…
Combinatorial Mutations and Block Diagonal Polytopes
Oliver Clarke, Akihiro Higashitani, Fatemeh Mohammadi
Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various famil…
Quadratic Gröbner bases of block diagonal matching field ideals and toric degenerations of Grassmannians
Akihiro Higashitani, Hidefumi Ohsugi
In the present paper, we prove that the toric ideals of certain -block diagonal matching fields have quadratic Gröbner bases. Thus, in particular, those are quadratically genera…
Cohomological rigidity for Fano Bott manifolds
Akihiro Higashitani, Kazuki Kurimoto
In the present paper, we characterize Fano Bott manifolds up to diffeomorphism in terms of three operations on matrix. More precisely, we prove that given two Fano Bott manifolds $…
Cohomological rigidity for toric Fano manifolds of small dimensions or large Picard numbers
Akihiro Higashitani, Kazuki Kurimoto, Mikiya Masuda
The cohomological rigidity problem for toric manifolds asks whether toric manifolds are diffeomorphic (or homeomorphic) if their integral cohomology rings are isomorphic. Many affi…
Homogeneous quandles arising from automorphisms of symmetric groups
Akihiro Higashitani, Hirotake Kurihara
Quandle is an algebraic system with one binary operation, but it is quite different from a group. Quandle has its origin in the knot theory and good relationships with the theory o…