Aspects of the (0,2)-McKay Correspondence

Abstract

<p>We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form $\CC^3/\ZZ_r$, focusing</p><p> on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number </p><p>of deformations of the tangent bundle for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the </p><p>G-Hilbert scheme, and note that this lower bound can be found using a combinatorial count of (0,2)-deformation moduli fields for</p><p>N=(2,2) conformal field theories on the orbifold. We also find that in general this minimum is not achieved, and expect the discrepancy </p><p>to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We show that </p><p>irreducible toric rational curves will account for some of the discrepancy, but also prove that there must be additional</p><p>worldsheet instanton corrections beyond those from smooth isolated rational curves.</p>