Before revision:  Ortner asked if an analogous result held for embeddability into a compact orientable surface \Sigma_g of genus g>0. In this paper we answer this question , under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircles in the collection.
After revision:  Ortner asked if an analogous result held for embeddability into orientable surfaces of higher genus. We answer this question , under an even more general definition of an arrangement, in which the pseudocircles in the collection are not required to intersect each other, or that the intersections are crossings: it suffices to have one pseudocircle that intersects all other pseudocircles in the collection.