Smooth G2 resolutions of non-free quotients of Calabi–Yau×S1

Determine whether non-free quotients of the form (X6 × S1)/Z2, obtained from a global involution that acts anti-holomorphically on the six-dimensional Calabi–Yau space X6 and reflects the circle S1, admit smooth G2 resolutions in general.

Background

In the massless type IIA dual frame, the seven-dimensional geometry is globally described by a Z2 quotient of X6 × S1. When the involution acts freely, one obtains smooth barely G2 manifolds. In the constructions considered here, the global action is not free, leading to singular quotients.

The authors note that while non-free quotients of this type can be defined, it is not established in general whether these singular spaces admit smooth G2 resolutions. Resolving this would clarify the geometric status of the backgrounds and potential uplifts to M-theory.