Using estimates of the distance and proper motion of Geminga and the constraints on its radial velocity posed by the shape of its bow shock, we investigate its birth place by tracing its space motion backwards in time. Our results exclude the lambda Ori association as the origin site because of the large distance between both objects at any time. Our simulations place the birth region at approximately 90-240 pc from the Sun, between 197 degrees and 199 degrees in Galactic longitude and -16 degrees and -8 degrees in latitude, most probably inside the Cas-Tau OB association or the Ori OB1a association. We discard the possibility of the progenitor being a massive field star. The association of Geminga with either stellar association implies an upper limit of M = 15 Msun for the mass of its progenitor. We also propose new members for the Cas-Tau and Ori OB1 associations.
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