Line Bundles and Curves on a del Pezzo Order

Details Line Bundles and Curves on a del Pezzo Order Line Bundles and Curves on a del Pezzo Order

2011-10-25

arxiv.org/abs/1110.5683v1

Mathematics

Algebraic Geometry

Scientific paper

Orders on surfaces provide a rich source of examples of noncommutative surfaces. Other than some existence results, very little is known about the various moduli spaces that can be associated to them. Even fewer examples have been explicitly computed. In this paper we compute the Picard and Hilbert schemes of an order on the projective plane ramified on a union of two conics. Our main result is that, upon carefully selecting the right Chern classes, the Hilbert scheme is a ruled surface over a genus two curve. Furthermore, this genus two curve is, in itself, the Picard scheme of the order.

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