Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards Mirror Symmetry for Varieties of General Type   The goal of this paper is to propose a theory of mirror symmetry for
varieties of general type. Using Landau-Ginzburg mirrors as motivation, we
describe the mirror of a hypersurface of general type (and more generally
varieties of non-negative Kodaira dimension) as the critical locus of the zero
fibre of a certain Landau-Ginzburg potential. The critical locus carries a
perverse sheaf of vanishing cycles. Our main results shows that one obtains the
interchange of Hodge numbers expected in mirror symmetry. This exchange is
between the Hodge numbers of the hypersurface and certain Hodge numbers defined
using a mixed Hodge structure on the hypercohomology of the perverse sheaf.
This exchange can be anticipated from an analysis of Hochschild homology of the
relevant categories arising in homological mirror symmetry in this case; we
also conjecture that a similar, but different, exchange of dimensions arises
from Hochschild cohomology, relating the cohomology of sheaves of polyvector
fields on the hypersurface to the cohomology of the critical locus.

32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph