Publications (24)
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…
Zeta functions of orders on surfaces
Daniel Chan, Sean B. Lynch
In this manuscript, we give effective methods for computing the zeta function of maximal orders on surfaces.
Moduli stacks of Serre stable representations in tilting theory
Daniel Chan, Boris Lerner
We introduce a new moduli stack, called the Serre stable moduli stack, which corresponds to studying families of point objects in an abelian category with a Serre functor. This all…
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 ind…
Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry
Daniel Chan
The Hilbert scheme of point modules was introduced by Artin-Tate-Van den Bergh to study non-commutative graded algebras. The key tool is the construction of a map from the algebra…
Non-commutative Mori contractions and $\PP^1$-bundles
Daniel Chan, Adam Nyman
We give a method for constructing maps from a non-commutative scheme to a commutative projective curve. With the aid of Artin-Zhang's abstract Hilbert schemes, this is used to cons…
Noncommutative linear systems and noncommutative elliptic curves
Daniel Chan, Adam Nyman
In this paper we introduce a noncommutative analogue of the notion of linear system, which we call a helix in an a…
Rational curves and ruled orders on surfaces
Daniel Chan, Kenneth Chan
We study ruled orders. These arise naturally in the Mori program for orders on projective surfaces and morally speaking are orders on a ruled surface ramified on a bisection and po…
Conic bundles and Clifford algebras
Daniel Chan, Colin Ingalls
We discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Br…
Low dimensional orders of finite representation type
Daniel Chan, Colin Ingalls
In this paper, we study noncommutative surface singularities arising from orders. The singularities we study are mild in the sense that they have finite representation type or, equ…
Numerically Calabi-Yau orders on surfaces
Daniel Chan, Rajesh Kulkarni
This is part of an ongoing program to classify maximal orders on surfaces via their ramification data. Del Pezzo and ruled orders have already been classified. In this paper, we cl…
A representation theoretic study of noncommutative symmetric algebras
Daniel Chan, Adam Nyman
We study Van den Bergh's noncommutative symmetric algebra (over division rings) via Minamoto's theory of Fano algebras. In particular, we show $\mathbb{S}^{nc}…
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…
2-hereditary algebras and almost Fano weighted surfaces
Daniel Chan
Tilting bundles on a weighted projective line have been intensively studied by representation theorists since they give rise to a derived equivalence bet…
A compact moduli of orbifold projective curves
Tarig Abdelgadir, Daniel Chan, Shinnosuke Okawa +1
We introduce the notion of stable orbifold projective curves, and show that the moduli stack of stable orbifold projective curves is isomorphic to the moduli stack of weighted poin…
Tensor stable moduli stacks and refined representations of quivers
Tarig Abdelgadir, Daniel Chan
In this paper, we look at the problem of modular realisations of derived equivalences, and more generally, the problem of recovering a Deligne-Mumford stack and a bund…
Moduli of bundles on exotic del Pezzo orders
Daniel Chan, Rajesh Kulkarni
Maximal orders of rank 4 on the projective plane, ramified on a smooth plane quartic are examples of exotic del Pezzo orders. We compute the possible Chern classes for line bundles…
Canonical singularities of orders over surfaces
Daniel Chan, Paul Hacking, Colin Ingalls
We classify the possible ramification data and etale local structure of orders over surfaces with canonical singularities.
Hilbert schemes for quantum planes are projective
Daniel Chan
We show that Hilbert schemes for quantum planes are projective.
McKay correspondence for canonical orders
Daniel Chan
Canonical orders, introduced in the minimal model program for orders, are simultaneous generalisations of Kleinian singularities and their associated skew group rings. In this pape…
Three-periodic helices on elliptic curves and their associated regular algebras
Daniel Chan, Adam Nyman
Let denote an algebraically closed field of characteristic zero and let denote a smooth elliptic curve over . Given a three-periodic elliptic helix $\underline{\mathcal{…
Two-periodic elliptic helices: classification and geometry
Daniel Chan, Adam Nyman
Let denote an algebraically closed field of characteristic zero and let denote a smooth elliptic curve over . In this paper, motivated by work in \cite{CN}, we think of…
Degenerations of orbifold curves as noncommutative varieties
Tarig Abdelgadir, Daniel Chan, Shinnosuke Okawa +1
Boundary points on the moduli space of pointed curves corresponding to collisions of marked points have modular interpretations as degenerate curves. In this paper, we study degene…
Terminal orders on arithmetic surfaces
Daniel Chan, Colin Ingalls
The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of…