132 citations · 204 across the 31 of their papers we have counts for
15 papers · 1 filter
Some terminal orders on 3-folds
Daniel Chan, Colin Ingalls
We produce the first known examples of non-trivial terminal local orders in the 3-dimensional case. We exhibit two different constructions. The first produces maximal orders with g…
A differential analogue of the wild automorphism conjecture
Jason Bell, Colin Ingalls, Rahim Moosa +1
A differential analogue of the conjecture of Reichstein, Rogalski, and Zhang in algebraic dynamics is here established: if is a projective variety over an algebraically closed…
On stacky surfaces and noncommutative surfaces
Eleonore Faber, Colin Ingalls, Shinnosuke Okawa +1
Let be an algebraically closed field of characteristic or zero. Let be a tame order of global dimension over a normal surface over $\mat…
The minimal model program for arithmetic surfaces enriched by a Brauer class
Daniel Chan, Colin Ingalls
We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class . When has prime index…
Explicit coverings of families of elliptic surfaces by squares of curves
Colin Ingalls, Adam Logan, Owen Patashnick
We show that, for each , there is a family of elliptic surfaces which are covered by the square of a curve of genus , and whose Hodge structures have an action by ${\mat…
Crepant resolutions of double covers: On the Cynk-Hulek criterion for crepant resolutions of double cover
Colin Ingalls, Adam Logan
A collection of divisors in a smooth variety is an {\em arrangement} if intersections of all subsets of are smooth. We show that a double cover of…
A McKay correspondence for reflection groups
Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls
We construct a noncommutative desingularization of the discriminant of a finite reflection group as a quotient of the skew group ring . If is generated by order two…
The minimal model program for b-log canonical divisors and applications
Daniel Chan, Kenneth Chan, Louis de Thanhoffer de Völcsey +8
We discuss the minimal model program for b-log varieties, which is a pair of a variety and a b-divisor, as a natural generalization of the minimal model program for ordinary log va…
Period-index bounds for arithmetic threefolds
Benjamin Antieau, Asher Auel, Colin Ingalls +2
The standard period-index conjecture for the Brauer group of a field of transcendence degree 2 over a -adic field predicts that the index divides the cube of the period. Using G…
Noncommutative resolutions of discriminants
Ragnar-Olaf Buchweitz, Eleonore Faber, Colin Ingalls
We give an introduction to the McKay correspondence and its connection to quotients of by finite reflection groups. This yields a natural construction of noncommutat…
On the Kodaira dimension of maximal orders
Nathan Grieve, Colin Ingalls
Let $\kk$ be an algebraically closed field of characteristic zero and $\KK$ a finitely generated field over $\kk$. Let be a central simple $\KK$-algebra, a normal projectiv…
Unramified Brauer classes on cyclic covers of the projective plane
Colin Ingalls, Andrew Obus, Ekin Ozman +1
Let X --> P^2 be a p-cyclic cover branched over a smooth, connected curve C of degree divisible by p, defined over a separably closed field of prime-to-p characteristic. We show th…
An Explicit Derived Equivalence of Azumaya Algebras on K3 Surfaces via Koszul Duality
Colin Ingalls, Madeeha Khalid
We consider moduli spaces of Azumaya algebras on K3 surfaces and construct an example. In some cases we show a derived equivalence which corresponds to a derived equivalence betwee…
On nodal Enriques surfaces and quartic double solids
Colin Ingalls, Alexander Kuznetsov
We consider the class of singular double coverings $X \to \PP^3$ ramified in the degeneration locus of a family of 2-dimensional quadrics. These are precisely the quartic doubl…
Rank Two Sheaves on K3 Surfaces: A Special Construction
Colin Ingalls, Madeeha Khalid
Let X be a K3 surface of degree 8 in P^5 with hyperplane section H. We associate to it another K3 surface M which is a double cover of P^2 ramified on a sextic curve C. In the gene…