## Canonical singularities for orders over surfaces

- CHI D. Chan, P. Hacking, C. Ingalls
- Proc. LMS
- 2009

- Published 2011

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 possibly some fibres. We describe fibres of a ruled order and show they are in some sense rational. We also determine the Hilbert scheme of rational curves and hence the corresponding non-commutative Mori contraction. This gives strong evidence that ruled orders are examples of the non-commutative ruled surfaces introduced by Van den Bergh. Throughout, we work over an algebraically closed base field k of characteristic zero.

@inproceedings{Chan2011RationalCA,
title={Rational curves and ruled orders on surfaces},
author={Daniel Chan and Kenneth Chan},
year={2011}
}