Advances in Theoretical and Mathematical Physics

Volume 20 (2016)

Number 5

$(0,2)$-deformations and the $G$-Hilbert scheme

Pages: 1083 – 1108



Benjamin Gaines (Department of Mathematics, Iona College, New Rochelle, New York, U.S.A.)


We study first-order deformations of the tangent sheaf of resolutions of Calabi–Yau threefolds that are of the form $\mathbb{C}^3 / \mathbb{Z}_r$, 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.

Published 17 January 2017