Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From semi-orthogonal decompositions to polarized intermediate Jacobians
  via Jacobians of noncommutative motives   Let X and Y be complex smooth projective varieties, and D^b(X) and D^b(Y) the
associated bounded derived categories of coherent sheaves. Assume the existence
of a triangulated category T which is admissible both in D^b(X) as in D^b(Y).
Making use of the recent theory of Jacobians of noncommutative motives, we
construct out of this categorical data a morphism t of abelian varieties (up to
isogeny) from the product of the intermediate algebraic Jacobians of X to the
product of the intermediate algebraic Jacobians of Y. When the orthogonal
complement of T in D^b(X) has a trivial Jacobian (e.g. when it is generated by
exceptional objects), the morphism t is split injective. When this also holds
for the orthogonal complement of T in D^b(Y), t becomes an isomorphism.
Furthermore, in the case where X and Y have a single intermediate algebraic
Jacobian carrying a principal polarization, we prove that the morphism t
preserves this extra structure. As an application, we obtain categorical
Torelli theorems, an incompatibility between two conjectures of Kuznetsov (one
concerning Fourier-Mukai functors and another one concerning Fano threefolds),
a new proof of a classical theorem of Clemens-Griffiths on blow-ups of
threefolds, and several new results on quadric fibrations and intersection of
quadrics.

34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an