Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hochschild cohomology versus the Jacobian ring, and the Torelli theorem
  for cubic fourfolds   The Jacobian ring J(X) of a smooth hypersurface determines its isomorphism
type. This has been used by Donagi and others to prove the generic global
Torelli theorem for hypersurfaces in many cases. In Voisin's original proof of
the global Torelli theorem for smooth cubic fourfolds the Jacobian ring does
not intervene. In this paper we present a proof of the global Torelli theorem
for cubic fourfolds that relies on the Jacobian ring and the (derived) global
Torelli theorem for K3 surfaces. It emphasizes, once again, the relation
between K3 surfaces and smooth cubic fourfolds. More generally, for a variant
of Hochschild cohomology of Kuznetsov's category (together with the degree
shift functor) associated with an arbitrary smooth hypersurface we construct a
graded ring homomorphism from the Jacobian ring to it, which is shown to be
bijective whenever Kuznetsov's category is a Calabi-Yau category.

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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin