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We discuss deformations of orbifold singularities on tilted tori in thecontext of Type IIA orientifold model building with D6-branes on specialLagrangian cycles. Starting from $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$, wemod out an additional $\mathbb{Z}_3$ symmetry to describe phenomenologicallyappealing backgrounds and reduce to $\mathbb{Z}_3$ and $\Omega\mathcal{R}$invariant orbits of deformations. While D6-branes carrying SO(2N) or USp(2N)gauge groups do not constrain deformations, D6-branes with U(N) gauge groupsdevelop non-vanishing D-terms if they couple to previously singular, nowdeformed cycles. We present examples for both types of D6-branes, and in athree-generation Pati-Salam model on $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_6')$we find that ten out of 15 twisted complex structure moduli are indeedstabilised at the orbifold point by the existence of the brane stacks.

Deformations on Tilted Tori and Moduli Stabilisation at the Orbifold Point