Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orthogonally spherical objects and spherical fibrations   We introduce a relative version of the spherical objects of Seidel and
Thomas. Define an object E in the derived category D(Z x X) to be spherical
over Z if the corresponding functor from D(Z) to D(X) gives rise to
autoequivalences of D(Z) and D(X) in a certain natural way. Most known examples
come from subschemes of X fibred over Z. This categorifies to the notion of an
object of D(Z x X) orthogonal over Z. We prove that such an object is spherical
over Z if and only if it has certain cohomological properties similar to those
in the original definition of a spherical object. We then interpret this
geometrically in the case when our objects are actual flat fibrations in X over
Z.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an