1 citations · 2 across the 8 of their papers we have counts for
10 papers
The rationality problem for hypersurfaces of degree at least five
James Hotchkiss
We prove that a very general hypersurface of degree at least five and any positive dimension does not have a decomposition of the diagonal, over an uncountable algebraically closed…
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…
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 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 $\ma…
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…
On decompositions for Fano schemes of intersections of two quadrics
Pieter Belmans, Jishnu Bose, Sarah Frei +6
We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelli…
The period-index problem for complex tori
James Hotchkiss
We solve the period-index problem for the Brauer group of a general complex torus of dimension at least three, giving an explicit formula for the index of each Brauer class. As a c…
Hodge theory of twisted derived categories and the period-index problem
James Hotchkiss
We study the Hodge theory of twisted derived categories and its relation to the period-index problem. Our main contribution is the development of a theory of twisted Mukai structur…
The gonality of complete intersection curves
James Hotchkiss, Chung Ching Lau, Brooke Ullery
The purpose of this paper is to show that for a complete intersection curve in projective space (other than a few stated exceptions), any morphism satis…