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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:…
The geometric Merkurjev-Panin Conjecture for the Cox category
Daniel Erman, Andrew Hanlon, Gaku Liu +1
We show that a strong version of the geometric Merkurjev-Panin conjecture holds for the Cox category of a projective toric variety. That is, we prove that the full strong exception…
Computing weighted sheaf cohomology using noncommutative differential modules
Michael K. Brown, Daniel Erman
We describe a novel method for computing sheaf cohomology over weighted projective spaces and stacks using exterior algebra and differential module techniques, generalizing an algo…
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 transfer principle for unirationality
Daniel Erman, Eric Riedl
We apply ideas related to the strength of polynomials to provide new cases of unirational hypersurfaces. It is famously known that hypersurfaces that are smooth in very high codime…