27 citations · 91 across the 18 of their papers we have counts for
10 papers · 1 filter
Cellular free resolutions for normalizations of toric ideals
Christine Berkesch, Lauren Cranton Heller, Gregory G. Smith +1
For any toric ideal in a polynomial ring , we provide a combinatorial description of a free resolution of the integral closure of the -module . These new complexes a…
Differential operators, retracts, and toric face rings
Christine Berkesch, C-Y. Jean Chan, Patricia Klein +3
We give explicit descriptions of rings of differential operators of toric face rings in characteristic . For quotients of normal affine semigroup rings by radical monomial ideal…
An illustrated view of differential operators of a reduced quotient of an affine semigroup ring
Christine Berkesch, C-Y. Jean Chan, Patricia Klein +3
Through examples, we illustrate how to compute differential operators on a quotient of an affine semigroup ring by a radical monomial ideal, when working over an algebraically clos…
Homological and combinatorial aspects of virtually Cohen--Macaulay sheaves
Christine Berkesch, Patricia Klein, Michael C. Loper +1
When studying a graded module over the Cox ring of a smooth projective toric variety , there are two standard types of resolutions commonly used to glean information: free r…
Syzygies, finite length modules, and random curves
Christine Berkesch, Frank-Olaf Schreyer
We apply the theory of Groebner bases to the computation of free resolutions over a polynomial ring, the defining equations of a canonically embedded curve, and the unirationality…
Three flavors of extremal Betti tables
Christine Berkesch, Daniel Erman, Manoj Kummini
We discuss extremal Betti tables of resolutions in three different contexts. We begin over the graded polynomial ring, where extremal Betti tables correspond to pure resolutions. W…