Aspinwall, PS, *A McKay-Like Correspondence for (0,2)-Deformations*, vol. 18 no. 4
(October, 2011),
pp. 761-797 [1110.2524], [1110.2524v3] .
**Abstract:**

*We present a local computation of deformations of the tangent bundle for a
resolved orbifold singularity C^d/G. These correspond to (0,2)-deformations of
(2,2)-theories. A McKay-like correspondence is found predicting the dimension
of the space of first-order deformations from simple calculations involving the
group. This is confirmed in two dimensions using the Kronheimer-Nakajima quiver
construction. In higher dimensions such a computation is subject to nontrivial
worldsheet instanton corrections and some examples are given where this
happens. However, we conjecture that the special crepant resolution given by
the G-Hilbert scheme is never subject to such corrections, and show this is
true in an infinite number of cases. Amusingly, for three-dimensional examples
where G is abelian, the moduli space is associated to a quiver given by the
toric fan of the blow-up. It is shown that an orbifold of the form C^3/Z7 has a
nontrivial superpotential and thus an obstructed moduli space.*