5 papers
The hyperkähler period-index conjecture is false
Pieter Belmans, James Hotchkiss
Huybrechts conjectured that for every Brauer class on a hyperkähler variety we have that , strengthening the usual p…
The Brauer group of a Stein algebra
Olivier Benoist, James Hotchkiss
We investigate the Brauer group of the ring of holomorphic functions on a finite-dimensional Stein space S. We provide a purely topological computation of this gro…
The period-index problem for hyper-Kähler varieties via hyperholomorphic bundles
James Hotchkiss, Davesh Maulik, Junliang Shen +2
We prove new bounds for the period-index problem for hyper-Kähler varieties of -type using projectively hyperholomorphic bundles constructed by Markman. We show that $\m…
Complexes of stable birational invariants
James Hotchkiss, David Stapleton
We introduce a new stable birational invariant, which takes the form of a functor sending a degenerating variety to the homotopy type of a chain complex. Our invariant is a categor…
The period-index conjecture for abelian threefolds and Donaldson-Thomas theory
James Hotchkiss, Alexander Perry
We prove the period-index conjecture for unramified Brauer classes on abelian threefolds. To do so, we develop a theory of reduced Donaldson-Thomas invariants for 3-dimensional Cal…