Rational curves and ruled orders on surfaces

2011/06/30 by Chan, Daniel, Chan, Kenneth
#14J99 #16H99 #Algebraic Geometry (math.AG) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1106.6086

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.

Related

• The Explicit Construction of Orders on Surfaces
• The Projective Theory of Ruled Surfaces
• Ruled and rational surfaces and their models
• Log terminal orders are numerically rational
• An explicit construction of ruled surfaces