Double covers and vector bundles of rank two

Abstract

In 2017, Catanese–Perroni gave a natural correspondence between the Picard group of a double cover and a set of pairs of a 2-bundle and a certain morphism of 2-bundles on the base space. In this paper, we describe the group structure of the latter set induced from the Picard group in terms of transition functions of 2-bundles. This study is derived from the study of embedded topology of plane curves. It also proposes approaches to the study of Picard groups of double covers, and to the construction of 2-bundles.