Minima of the local recurrence time, TL(M), are correlated with the locations of historical main shocks in the San Jacinto (SJ)-Elsinore (E) fault zones of southern California. We define TL(M) as the recurrence time calculated from the local b and a values of the frequency-magnitude distribution (earthquakes within 6 and 10 km from each point in the SJ and E fault zones, respectively). We propose that anomalously low TL(M) values map asperities. Out of six historic main shocks (1899--1968), five ruptured substantial parts of four asperities mapped by our method, which uses solely the modern earthquake catalog (M≥1.2, 1981.0--1998.8). We estimate the probability for this correlation to occur at random as ~10-2 to 10-3, depending on the scenario chosen. It appears that the minima in TL(M) are tied to minima in b values more than to maxima in a values. Thus locations of low b values can also be used as an indication where asperities may be located and where main shocks are most likely. The Anza gap, a segment of the San Jacinto fault with low a values, is mapped as an asperity by our method. The heterogeneity in b values is strong throughout the study area. The b values range from 0.5 to 1.8 over distances of 10 km. Volumes with approximately constant b values have radii of r=8¿6 km. Our results suggest that detailed mapping of b values and local recurrence times in volumes with a few kilometers radius reveals important information about the local seismic hazard, hitherto untapped by conventional seismicity analyses. ¿ 2000 American Geophysical Union