The integration of a high share of solar photovoltaics (PV) in distribution networks requires advanced voltage control technologies or network augmentation, both associated with significant investment costs. An alternative is to prevent new customers from installing solar PV systems, but this is against the common goal of increasing renewable energy generation. This paper demonstrates that solar PV curtailment in low voltage areas can be reduced and fairly distributed among PV owners by centrally coordinating the operation of PV inverters. The optimal inverter active and reactive power operation points are computed by solving a multi-objective optimization problem with a fairness objective. The main results show that fair optimal inverter dispatch (FOID) results in less power curtailment than passive voltage regulation based on Volt/VAr droop control, especially at high solar PV to load ratios. The effectiveness of the model is demonstrated on a residential low voltage network.