Minimal flux Minkowski classification

We classify Minkowski${}_4$ solutions in type IIA supergravity, with N=2 supersymmetry and an SU(2) R-symmetry of a certain type. Many subcases can be reduced to relatively simple PDEs, among which we recover various intersecting brane systems, and AdS${}_d$ solutions, $d=5,6,7$, and in particular the recently found general massive AdS${}_7$ solutions. Imposing compactness of the internal six-manifold we obtain promising solutions with localized D-branes and O-planes.