Population genomic analyses of Midas cichlid fishes in young Nicaraguan crater lakes suggest that sympatric speciation is promoted by polygenic architectures. The transition from 'well-marked varieties' of a single species into 'well-defined species'-especially in the absence of geographic barriers to gene flow (sympatric speciation)-has puzzled evolutionary biologists ever since Darwin(1,2). Gene flow counteracts the buildup of genome-wide differentiation, which is a hallmark of speciation and increases the likelihood of the evolution of irreversible reproductive barriers (incompatibilities) that complete the speciation process(3). Theory predicts that the genetic architecture of divergently selected traits can influence whether sympatric speciation occurs(4), but empirical tests of this theory are scant because comprehensive data are difficult to collect and synthesize across species, owing to their unique biologies and evolutionary histories(5). Here, within a young species complex of neotropical cichlid fishes (Amphilophus spp.), we analysed genomic divergence among populations and species. By generating a new genome assembly and re-sequencing 453 genomes, we uncovered the genetic architecture of traits that have been suggested to be important for divergence. Species that differ in monogenic or oligogenic traits that affect ecological performance and/or mate choice show remarkably localized genomic differentiation. By contrast, differentiation among species that have diverged in polygenic traits is genomically widespread and much higher overall, consistent with the evolution of effective and stable genome-wide barriers to gene flow. Thus, we conclude that simple trait architectures are not always as conducive to speciation with gene flow as previously suggested, whereas polygenic architectures can promote rapid and stable speciation in sympatry.