21 citations · 64 across the 17 of their papers we have counts for
7 papers · 1 filter
Nonnoetherian coordinate rings with unique maximal depictions
Charlie Beil
A depiction of a nonnoetherian integral domain is a special coordinate ring that provides a framework for describing the geometry of . We show that if is noetherian in c…
Nonnoetherian singularities and their noncommutative blowups
Charlie Beil
We establish a new fundamental class of varieties in nonnoetherian algebraic geometry related to the central geometry of dimer algebras. Specifically, given an affine algebraic var…
Nonlocality and the central geometry of dimer algebras
Charlie Beil
Let be a dimer algebra and its center. It is well known that if is cancellative, then and are noetherian and is a finitely generated -module. Here we sho…
Cancellativization of dimer models
Charlie Beil, Akira Ishii, Kazushi Ueda
We show that any dimer model can be made cancellative without changing the characteristic polygon.
Nonnoetherian geometry
Charlie Beil
We introduce a theory of geometry for nonnoetherian commutative algebras with finite Krull dimension. In particular, we establish new notions of normalization and height: depiction…
The Geometry of Noncommutative Singularity Resolutions
Charlie Beil
We introduce a geometric realization of noncommutative singularity resolutions. To do this, we first present a new conjectural method of obtaining conventional resolutions using co…