Line-Bundle-Valued Ternary Quadratic Bundles Over Schemes

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dc.creatorEesanaipaadi, Venkata Balaji Thiruvalloor
dc.date2005-06-08
dc.date2005-07-24
dc.date.accessioned2026-07-07T05:20:36Z
dc.date.available2026-07-07T05:20:36Z
dc.descriptionWe describe a satisfactory theory of degeneration of quadratic forms in three variables in the most general setting possible: the quadratic forms are defined on rank 3 vector bundles over an arbitrary scheme and could have values in nontrivial line bundles. Our results extend what is known for good forms; for example we show that the Witt-invariant suffices for classification. We determine explicitly the general, special and usual orthogonal groups and present applications. We indicate examples of rank 4 vector bundles that do not admit any Azumaya structures and of rank 3 vector bundles that do not admit any good quadratic forms with values in specified line bundles. These examples occur naturally on the Seshadri-desingularisations of moduli spaces of rank two degree zero vector bundles over a curve relative to an integral normal locally-Nagata (universally Japanese) base scheme.
dc.description79 pages; PDFLaTeX; improved exposition; new result included--isomorphism of the Picard group of the base with that of the scheme of specialised algebras; some typos and cross-references corrected
dc.identifierhttps://arxiv.org/abs/math/0506146
dc.identifierhttp://arxiv.org/abs/math/0506146
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75436
dc.subjectAlgebraic Geometry
dc.subjectRings and Algebras
dc.subject14A25, 14F05, 14L15, 14M, 14Q, 15A63, 15A66, 15A75, 15A78, 16H05, 16S60, 16W20, 20G05, 20G35
dc.titleLine-Bundle-Valued Ternary Quadratic Bundles Over Schemes
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