3 papers
math.AG2026
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:…
math.AC2025
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…
math.AG2025
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…