GIT Quotients of Products of Projective Planes

Abstract

We study the quotients for the diagonalaction of _SL_3(C) on the n-fold product of P2(C):we are interested in describing how the quotient changes when wevary the polarization (i.e. the choice of an ample linearized linebundle). We illustrate the different techniques for the constructionof a quotient, in particular the numerical criterion forsemi-stability and the “elementary transformations” which areresolutions of precisely described singularities (case n = 6).