A recursion for counts of real curves in CP^(2n-1): another proof

In a recent paper, we obtained a WDVV-type relation for real genus 0 Gromov-Witten invariants with conjugate pairs of insertions; it specializes to a complete recursion in the case of odd-dimensional projective spaces. This note provides another, more complex-geometric, proof of the latter. The main part of this approach readily extends to real symplectic manifolds with empty real locus, but not to the general case.