Conic bundles and Clifford algebras

Daniel Chan; Colin Ingalls

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arXiv · 1101.1705

Conic bundles and Clifford algebras

Daniel Chan·Colin Ingalls

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Abstract

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.

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Daniel Chan, Colin Ingalls. 2011-01-10. Conic bundles and Clifford algebras. https://arxiv.org/abs/1101.1705

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