English

Rational curves and ruled orders on surfaces

Rings and Algebras 2011-07-01 v1 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1106.6086,
  title  = {Rational curves and ruled orders on surfaces},
  author = {Daniel Chan and Kenneth Chan},
  journal= {arXiv preprint arXiv:1106.6086},
  year   = {2011}
}
R2 v1 2026-06-21T18:29:30.423Z