Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Line-Bundle-Valued Ternary Quadratic Bundles Over Schemes   We 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.

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The categories of this paper are: cs
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The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int