Baro González, ElíasFernando Galván, José FranciscoGamboa Mutuberria, José Manuel2025-12-012025-12-01202110.1007/s13163-020-00377-5https://hdl.handle.net/20.500.14352/128236In this article we prove that a semialgebraic map from M to N is a branched covering if and only if its associated spectral map is a branched covering. In addition, such spectral map has a neat behavior with respect to the branching locus, the ramification set and the ramification index. A crucial fact to prove the preceding result is the characterization of the prime ideals whose fibers under the previous spectral map are singletons.engjournal articlehttps://doi.org/10.1007/s13163-020-00377-5open accessSemialgebraic setSemialgebraic functionBranched coveringBranching locusRamification setRamification indexZariski spectraSpectral mapCollapsing setMatemáticas (Matemáticas)1201.01 Geometría Algebraica