(0,2)-Deformations and the $G$-Hilbert Scheme

Abstract

We study first order deformations of the tangent sheaf of resolutions of Calabi-Yau threefolds that are of the form ${\mathbb{C}}^3/Z_r$, focusing on the cases where the orbifold has an isolated singularity. We prove a lower bound on the number of deformations for any crepant resolution of this orbifold. We show that this lower bound is achieved when the resolution used is the G-Hilbert scheme, and note that this lower bound can be found using methods from string theory. These methods lead us to a new way to construct the G-Hilbert scheme using the singlet count.

20 pages, 7 figures

References in corpus (1)

• A McKay-Like Correspondence for (0,2)-Deformations

Cited by in corpus (1)

• Rational Curves and (0,2)-Deformations