King's Conjecture and the Cox category
Algebraic Geometry
2025-12-19 v3 Commutative Algebra
Abstract
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 extends ideas of Beilinson and Bondal to all semiprojective toric varieties.
Cite
@article{arxiv.2501.00130,
title = {King's Conjecture and the Cox category},
author = {Matthew R. Ballard and Christine Berkesch and Michael K. Brown and Lauren Cranton Heller and Daniel Erman and David Favero and Sheel Ganatra and Andrew Hanlon and Jesse Huang},
journal= {arXiv preprint arXiv:2501.00130},
year = {2025}
}
Comments
Updates include a number of new references and minor edits. 55 pages, 7 figures