11 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…