In this paper we present a spatial stochastic model for genetic recombination, that answers if diversity is preserved in an infinite population of recombinating individuals distributed spatially. We show that, for finite times, recombination may maintain all the various potential different types, but when time grows infinitely, the diversity of individuals extinguishes off. So under the model premisses, recombination and spatial localization alone are not enough to explain diversity in a population. Further we discuss an application of the model to a controversy regarding the diversity of "Major Histocompatibility Complex" (MHC).