Espaços de Moduli de complexos quadráticos e de suas superfícies singulares

Abstract

A quadratic line complex, or a quadratic complex, is by definition a set of lines in a projective space Pn (n = 3, in our case) which satisfy a given quadratic equation. A quadratic complex can also be considered as a pencil of quadrics. Hence, it has a well defined Segre symbol. It is a classical fact that lines of a given complex through any point p ∈P3 form in general a quadratic cone. The points such that theses cones break up into two planes form a surface, the Singular Surface of the complex. The objective of this work is, for a fixed Segre symbol, to construct the Moduli space of quadratic complex, the Moduli space of corresponding singular surfaces and to study the relation between them.