Spectral maps associated to semialgebraic branched coverings

Abstract

In 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.