Rational curves and ruled orders on surfaces

Details Rational curves and ruled orders on surfaces Rational curves and ruled orders on surfaces

2011-06-30

arxiv.org/abs/1106.6086v1

Mathematics

Rings and Algebras

Scientific paper

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.

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