%0 Journal Article
%T Conic bundles and Clifford algebras
%A Daniel Chan
%A Colin Ingalls
%J Mathematics
%D 2011
%I arXiv
%X We discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. We then restrict to a surface base and we express the second Chern class of the order in terms $K^3$ and other invariants of the corresponding conic bundle. We find the conic bundles corresponding to minimal del Pezzo quaterion orders and we discuss problems concerning their moduli.
%U http://arxiv.org/abs/1101.1705v1