Rational curves and ruled orders on surfaces

JOURNAL OF ALGEBRA

卷:435

Article

Chan, Daniel¹  Chan, Kenneth² 

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

关键词: Noncommutative algebraic geometry;    Maximal order;    Noncommutative algebra;    Moduli;    Azumaya algebra;    Ruled surface;   

DOI  :  10.1016/j.jalgebra.2015.03.018

来源: Elsevier

【 摘 要 】

We study ruled orders. These arise naturally in the Maori 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 Maori 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. Crown Copyright (C) 2015 Published by Elsevier Inc. All rights reserved.

【 授权许可】

Free