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

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