@UNPUBLISHED{publication1, title = "Construction of algebraic covers", author = "{DIAS, Eduardo}", year = "2017-11-28", abstract = " Given an algebraic variety Y and a locally free OY-module of rank 2, E, Miranda defined the notion of triple cover homomorphism as a map S2E \→ E that determines a triple cover of Y . In this paper we generalize the definition of cover homomorphism and present a method to compute them. The main theorem shows how to use cover homomorphisms to describe the section ring of polarized varieties (X,L) when L induces a covering map. Furthermore, we study in detail the case of Gorenstein covering maps for which the direct image of OX admits an orthogonal decomposition. Finally we apply the results to determine Gorenstein covers of degree 6 satisfying some mild conditions, obtaining the structure of a codimension 4 Gorenstein ideal, and study the ideals that determine a S3-Galois branched cover. ", url = "http://www.mat.uc.pt/preprints/eng\_2017.html", note = "" }