Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mirror symmetry for weighted projective planes and their noncommutative
  deformations   We study the derived categories of coherent sheaves of weighted projective
spaces and their noncommutative deformations, and the derived categories of
Lagrangian vanishing cycles of their mirror Landau-Ginzburg models. In
particular, we show that the derived category of coherent sheaves (B-branes) on
the weighted projective plane $\CP^2(a,b,c)$ is equivalent to the derived
category of vanishing cycles (A-branes) on the affine hypersurface
$X=\{x^ay^bz^c=1\}\subset (\C^*)^3$ equipped with an exact symplectic form and
the superpotential $W=x+y+z$. Hence, the homological mirror symmetry conjecture
holds for weighted projective planes. Moreover, we also show that this mirror
correspondence between derived categories can be extended to toric
noncommutative deformations of $\CP^2(a,b,c)$ where B-branes are concerned, and
their mirror counterparts, non-exact deformations of the symplectic structure
of $X$ where A-branes are concerned. We also obtain similar results for other
examples such as weighted projective lines or Hirzebruch surfaces.

26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph