Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadric bundles and hyperbolic equivalence   We introduce the notion of hyperbolic equivalence for quadric bundles and
show that hyperbolic equivalent quadric bundles share many important
properties: they have the same Brauer data; moreover, if they have the same
dimension over the base, they are birational over the base and have equal
classes in the Grothendieck ring of varieties.
  Furthermore, when the base is a projective space we show that two quadric
bundles are hyperbolic equivalent if and only if their cokernel sheaves are
isomorphic up to twist, their fibers over a fixed point of the base are Witt
equivalent, and, in some cases, certain quadratic forms on intermediate
cohomology groups of the underlying vector bundles are Witt equivalent. For
this we show that any quadric bundle over $\mathbb{P}^n$ is hyperbolic
equivalent to a quadric bundle whose underlying vector bundle has many
cohomology vanishings; this class of bundles, called VLC bundles in the paper,
is interesting by itself.

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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex