12 citations · 28 across the 16 of their papers we have counts for
16 papers
Variations of GIT Quotients and Dimer Combinatorics for Toric Compound Du Val Singularities
Yusuke Nakajima
A dimer model is a bipartite graph described on the real two-torus, from which we can define the associated quiver. It is known that for any three-dimensional Gorenstein toric sing…
Combinatorial mutations of Newton-Okounkov polytopes arising from plabic graphs
Akihiro Higashitani, Yusuke Nakajima
It is known that the homogeneous coordinate ring of a Grassmannian has a cluster structure, which is induced from the combinatorial structure of a plabic graph. A plabic graph is a…
Lower bounds on Hilbert--Kunz multiplicities and maximal F-signatures
Jack Jeffries, Yusuke Nakajima, Ilya Smirnov +2
Hilbert-Kunz multiplicity and F-signature are numerical invariants of commutative rings in positive characteristic that measure severity of singularities: for a regular ring both i…
Generalized F-signatures of Hibi rings
Akihiro Higashitani, Yusuke Nakajima
The -signature is a numerical invariant defined by the number of free direct summands in the Frobenius push-forward, and it measures singularities in positive characteristic. It…
Deformations of Dimer Models
Akihiro Higashitani, Yusuke Nakajima
The combinatorial mutation of polygons, which transforms a given lattice polygon into another one, is an important operation to understand mirror partners for two-dimensional Fano…
On 2-representation infinite algebras arising from dimer models
Yusuke Nakajima
The Jacobian algebra arising from a consistent dimer model is a bimodule -Calabi-Yau algebra, and its center is a -dimensional Gorenstein toric singularity. A perfect matchin…
Non-commutative crepant resolutions of Hibi rings with small class group
Yusuke Nakajima
In this paper, we study splitting (or toric) non-commutative crepant resolutions (= NCCRs) of some toric rings. In particular, we consider Hibi rings, which are toric rings arising…
Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
Akihiro Higashitani, Yusuke Nakajima
In this paper, we study divisorial ideals of a Hibi ring which is a toric ring arising from a partially ordered set. We especially characterize the special class of divisorial idea…
Semi-steady non-commutative crepant resolutions via regular dimer models
Yusuke Nakajima
A consistent dimer model gives a non-commutative crepant resolution (= NCCR) of a -dimensional Gorenstein toric singularity. In particular, it is known that a consistent dimer m…
Remarks on divisorial ideals arising from dimer models
Yusuke Nakajima
The Jacobian algebra arising from a consistent dimer model is derived equivalent to crepant resolutions of a -dimensional Gorenstein toric singularity , and it i…
Mutations of splitting maximal modifying modules: The case of reflexive polygons
Yusuke Nakajima
It is known that every three dimensional Gorenstein toric singularity has a crepant resolution. Although it is not unique, all crepant resolutions are connected by repeating the op…
On steady non-commutative crepant resolutions
Osamu Iyama, Yusuke Nakajima
We introduce special classes of non-commutative crepant resolutions (= NCCR) which we call steady and splitting. We show that a singularity has a steady splitting NCCR if and only…
Ulrich modules over cyclic quotient surface singularities
Yusuke Nakajima, Ken-ichi Yoshida
In this paper, we characterize Ulrich modules over cyclic quotient surface singularities by using the notion of special Cohen-Macaulay modules. We also investigate the number of in…
Dual F-signature of Cohen-Macaulay modules over rational double points
Yusuke Nakajima
The dual -signature is a numerical invariant defined via the Frobenius morphism in positive characteristic. It is known that the dual -signature characterizes some singularit…
Dual F-signature of special Cohen-Macaulay modules over cyclic quotient surface singularities
Yusuke Nakajima
The notion of -signature is defined by C. Huneke and G. Leuschke and this numerical invariant characterizes some singularities. This notion is extended to finitely generated mod…
Generalized F-signature of invariant subrings
Mitsuyasu Hashimoto, Yusuke Nakajima
It is known that a certain invariant subring has finite -representation type. Thus, we can write the -module as a finite direct sum of finitely many -modules.…