Moduli de feixes de quádricas e de formas binárias

Abstract

The main objective is to study the relationship between space Moduli of pencil of quadrics, and Moduli space of binary forms. This study was based on article (AVRITZER; LANGE, 2000). In general, a Moduli space is an algebraic variety that parametrizes a collection of objects C, modulo an equivalence relation. In our case, C is the set of pencil of quadrics or set of binary forms of degree (n + 1), and the equivalence relation is to belong to the same orbit by the action of a group G. To establish the relationship between these spaces is important to consider the Segre symbol of which is an invariant of pencils of quadrics. Furthermore, we studied the normal form, a way to rewrite the pencil of quadrics, which easily met the Segre symbol, action of groups, in order to classify a pencil of quadric and a binary form as stable or semistable unstable, and quotient categorical, since the spaces's moduli are obtained by quotient.