Line Bundles and Curves on a del Pezzo Order
Algebraic Geometry
2013-05-14 v1 Rings and Algebras
Abstract
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.
Keywords
Cite
@article{arxiv.1110.5683,
title = {Line Bundles and Curves on a del Pezzo Order},
author = {Boris Lerner},
journal= {arXiv preprint arXiv:1110.5683},
year = {2013}
}