27 citations · 91 across the 18 of their papers we have counts for
20 papers
Nonsimplicial toric Nullstellensatz and stacky GKZ theory
Christine Berkesch, Daniel Erman, David Favero
We introduce a variant of the Cox ring using -Cartier divisors and use this to remedy various deficiencies of nonsimplicial toric varieties. Our main applications are:…
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…
King's Conjecture and the Cox category
Matthew R. Ballard, Christine Berkesch, Michael K. Brown +6
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective…
A sharp bound for hypergeometric rank in dimension three
Christine Berkesch, María-Cruz Fernández-Fernández
We provide a sharp upper bound on the quotient of the rank of an A-hypergeometric system with a three-dimensional torus action by the normalized volume of A; in this case, the uppe…
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…