Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Construction of algebraic covers
Publication Date:	2017-11-28
Authors:	- Eduardo Manuel Dias
Abstract:	Given an algebraic variety Y and a locally free O_Y-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 O_X 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.
Institution:	DMUC 17-50
Online version:	http://www.mat.uc.pt...prints/eng_2017.html
Download:	Not available