We present a detailed analysis of the electrostatic built-in field, the electronic structure, and the optical properties of a-plane GaN/AlN quantum dots with an arrowhead-shaped geometry. This geometry is based on extensive experimental analysis given in the literature. Our results indicate that the spatial overlap of electron and hole ground state wave functions is significantly increased, compared to that of a c-plane system, when taking the experimentally suggested trapezoid-shaped dot base into account. This finding is in agreement with experimental data on the optical properties of a-plane GaN/AlN quantum dots. (C) 2012 American Institute of Physics. (http://dx.doi.org/10.1063/1.4752108