Resolution of orbifold singularities on twisted seven-tori solvmanifolds

Ascertain a rigorous resolution method for the orbifold singularities of twisted seven-torus solvmanifolds (the twisted T7 quotiented by shifted Z2^3 actions such as \hat{Γ} and \check{Γ}), by constructing explicit blow-up procedures compatible with the co-closed G2-structure and the O5 orientifold involution. Provide a detailed local and global description of the resolved geometry that remains consistent with flux quantization and the intended type IIB AdS3 compactifications.

Background

The paper builds type IIB AdS3 solutions on twisted seven-torus solvmanifolds (co-closed G2-structure) quotiented by specific shifted Z23 orbifolds to reduce forms and control orientifold content. While Joyce’s criteria ensure blow-up procedures for certain flat T7 orbifolds with shifts, the extension of such resolutions to the corresponding twisted tori is not fully established.

The author notes that a blow-up procedure analogous to the flat case might resolve these singularities on twisted tori, but emphasizes that this remains unclear and requires explicit construction to ensure compatibility with the solvmanifold structure, orientifold planes, and fluxes.

References

Although it is not entirely clear how the orbifold singularities of the twisted tori should be resolved, one could expect that a blow-up procedure, similarly for flat \mathbb{T}7's, might do so.

— Supersymmetric scale-separated AdS$_3$ orientifold vacua of type IIB (2502.04791 - Hemelryck, 7 Feb 2025) in Section 5 (Summary)