Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrangian Floer superpotentials and crepant resolutions for toric
  orbifolds   We investigate the relationship between the Lagrangian Floer superpotentials
for a toric orbifold and its toric crepant resolutions. More specifically, we
study an open string version of the crepant resolution conjecture (CRC) which
states that the Lagrangian Floer superpotential of a Gorenstein toric orbifold
$\mathcal{X}$ and that of its toric crepant resolution $Y$ coincide after
analytic continuation of quantum parameters and a change of variables. Relating
this conjecture with the closed CRC, we find that the change of variable
formula which appears in closed CRC can be explained by relations between open
(orbifold) Gromov-Witten invariants. We also discover a geometric explanation
(in terms of virtual counting of stable orbi-discs) for the specialization of
quantum parameters to roots of unity which appears in Y. Ruan's original CRC
["The cohomology ring of crepant resolutions of orbifolds", Gromov-Witten
theory of spin curves and orbifolds, 117-126, Contemp. Math., 403, Amer. Math.
Soc., Providence, RI, 2006]. We prove the open CRC for the weighted projective
spaces $\mathcal{X}=\mathbb{P}(1,\ldots,1,n)$ using an equality between open
and closed orbifold Gromov-Witten invariants. Along the way, we also prove an
open mirror theorem for these toric orbifolds.

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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: acc-phys
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs
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The categories of this paper are: nlin