Espaço de moduli das configurações de desargues

Abstract

The main aim of this work is to study the moduli space of Desargues configurations and it was based in (AVRITZER; LANGE, 2002). A configurations of 10 points and 10 line of the classic Desargues Theorem is called a Desargues configuration. Many moduli spaces, if not all, are obtained algebraically through the quotient of algebraic varieties. So we have studied a little about Geometric Invariant Theory and actions of algebraic group on varieties. We have showed that there exist the categorical quotient of a algebraic variety X by a finite algebraic group G and that it is a coarse moduli space. Moreover, we have showed that if X is a affine (resp. quasi-projective) the categorical quotient is an affine (resp. quasi-projective) variety Finally, we proved that the categorical quotient (MD,p) of the ˇP3 by the algebraic group finite S5 is the moduli space coarse for the Desargues configurations.