Superfı́cies cúbiques i corbes quàrtiques

Abstract

[en] In Algebraic Geometry numbers 27 and 28 are usually associated with two well-known classical results. All smooth cubic surfaces contain 27 distinct lines. And all smooth plane quartics have 28 bitangents. The aim of this work is to stablish a relation between these two statements. First, we have introduced the theoretical basis needed to demonstrate the two classical results. In the final part, we have suggested a method with which the 27 lines contained in a cubic surface can be transformed into bitangents of a plane quartic and, also from the surface, an additional bitangent can be formed, so that we ultimately obtain the 28 bitangents.