2 citations · 8 across the 28 of their papers we have counts for
29 papers · 1 filter
Hook algebras and determinantal varieties
Steven V Sam, Keller VandeBogert, Jerzy Weyman
In characteristic zero, we prove that the Tor algebras of the generic, symmetric, and skew-symmetric determinantal rings are Koszul with respect to a natural regrading. In particul…
Carlsson's Conjecture and the Generalized Total Rank Conjecture in Characteristic Two
Keller VandeBogert
We prove the generalized total rank conjecture over regular rings in characteristic : if is a regular Noetherian domain of characteristic and is a differential -m…
Flagged Perturbations and Anchored Resolutions
Keller VandeBogert
In this paper, we take advantage of a reinterpretation of differential modules admitting a flag structure as a special class of perturbations of complexes. We are thus able to leve…
From total positivity to pure free resolutions
Steven V Sam, Keller VandeBogert
Using the Jacobi-Trudi identity as a base, we establish parallels between the theory of totally positive integer sequences and Koszul algebras. We then focus on the case of quadric…
Differential modules and Deformations of Free Complexes
Maya Banks, Keller VandeBogert
We classify (up to quasi-isomorphism) the free differential modules whose homology is equal to a given module by developing a theory for deforming an arbitrary free complex int…
The Total Rank Conjecture in Characteristic Two
Keller VandeBogert, Mark E. Walker
The Total Rank Conjecture is a coarser version of the Buchsbaum-Eisenbud-Horrocks conjecture which, loosely stated, predicts that modules with large annihilators must also have ``l…
Ribbon Schur Functors
Keller VandeBogert
We investigate a generalization of the classical notion of a Schur functor associated to a ribbon diagram. These functors are defined with respect to an arbitrary algebra, and in t…
Equivariant resolutions over Veronese rings
Ayah Almousa, Michael Perlman, Alexandra Pevzner +2
Working in a polynomial ring where is an arbitrary commutative ring with , we consider the Veronese subalgebras ,…
Differential Modules with Complete Intersection Homology
Maya Banks, Keller VandeBogert
Differential modules are natural generalizations of complexes. In this paper, we study differential modules with complete intersection homology, comparing and contrasting the theor…
A GL-Equivariant Complex Inducing Character Identities for Schur Modules
Keller VandeBogert
In this paper we construct a GL-equivariant complex of Schur modules over a ring of positive characteristic that can be used to deduce classical alternating sum identities for Schu…
Detecting Golodness via Gröbner Degeneration
Keller VandeBogert
In this paper we study the extent to which Golodness may be transferred along morphisms of DG-algebras. In particular, we show that if is a so-called fiber invariant ideal, the…
Polarizations and Hook Partitions
Ayah Almousa, Keller VandeBogert
In this paper, we relate combinatorial conditions for polarizations of powers of the graded maximal ideal with rank conditions on submodules generated by collections of Young table…
Products of Ideals and Golod Rings
Keller VandeBogert
In this paper, we study conditions guaranteeing that a product of ideals defines a Golod ring. We show that for a -dimensional regular local ring (or -variable polynomial rin…
On Restricted Powers of Complete Intersections
Keller VandeBogert
A restricted th power of an ideal is obtained by restricting the exponent vectors allowed to appear on the "natural" generating set of , for some integer . In this p…
On Constructions Related to the Generalized Taylor Complex
Keller VandeBogert
In this paper, we extend constructions and results for the Taylor complex to the generalized Taylor complex constructed by Herzog. We construct an explicit DG-algebra structure on…
Iterated Mapping Cones for Strongly Koszul Algebras
Keller VandeBogert
In this paper we extend the well-known iterated mapping cone procedure to monomial ideals in strongly Koszul algebras. We study properties of ideals generated by monomials in commu…
Linear Strands Supported on Regular CW Complexes
Keller VandeBogert
In this paper, we study ideals whose linear strand can be supported on a regular CW complex. We provide a sufficient condition for the linear strand of an arbitrary subideal of…
Linear Strands of Initial Ideals of Determinantal Facet Ideals
Ayah Almousa, Keller VandeBogert
A determinantal facet ideal (DFI) is an ideal generated by maximal minors of a generic matrix parametrized by an associated simplicial complex . In this paper, we construc…
DG Structure on Length 3 Trimming Complexes and Applications to Tor Algebras
Keller VandeBogert
In this paper, we consider the iterated trimming complex associated to data yielding a complex of length . We compute an explicit algebra structure in this complex in terms of t…
Vanishing of Avramov Obstructions for Products of Sequentially Transverse Ideals
Keller VandeBogert
Two ideals and are called transverse if . We show that the obstructions defined by Avramov for classes of (sequentially) transverse ideals in regular local r…
The DG Products of Peeva and Srinivasan Coincide
Keller VandeBogert
Consider the ideal , where is any field. This ideal can be resolved by both the -complexes of Buchsbaum and Eisenbud,…
Minimal Free Resolutions of Certain Equigenerated Monomial Ideals
Keller VandeBogert
Let denote the standard graded polynomial ring over a field . We study certain classes of equigenerated monomial ideals with the property that the so-…
Determinantal Facet Ideals for Smaller Minors
Ayah Almousa, Keller VandeBogert
A determinantal facet ideal (DFI) is generated by a subset of the maximal minors of a generic matrix where indexed by the facets of a simplicial complex .…
DG Structure on the Length 4 Big From Small Construction
Keller VandeBogert
The big from small construction was introduced by Kustin and Miller and can be used to construct resolutions of tightly double linked Gorenstein ideals. In this paper, we expand on…