5 citations · 5 across the 1 of their papers we have counts for
5 papers
Characterizing Multigraded Regularity and Virtual Resolutions on Products of Projective Spaces
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi
We explore the relationship between multigraded Castelnuovo--Mumford regularity, truncations, Betti numbers, and virtual resolutions on a product of projective spaces . After pr…
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…
Seshadri Regions and the Asymptotic Shape of Multigraded Regularity
Juliette Bruce, Lauren Cranton Heller, Mahrud Sayrafi +1
We introduce the Seshadri region of a subvariety, a convex region packaging the classical Seshadri constants with respect to every line bundle simultaneously. We develop the theory…
Explicit constructions of short virtual resolutions of truncations
Lauren Cranton Heller
We propose a concept of truncation for arbitrary smooth projective toric varieties and construct explicit cellular resolutions for nef truncations of their total coordinate rings.…