2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160726These are notes on the construction of the GIT-fans for quivers without oriented cycles. We follow closely the steps outlined by N. Ressayre in "The GIT-Equivalence for G-Line Bundles" (Geometriae Dedicata, Volume 81, Numbers 1-3, 2000). A simple construction of the GIT-fan for normal, affine G-varities has been recently given by Ivan V. Arzhantsev and Juergen Hausen in "Geometric Invariant Theory via Cox Rings"Representation TheoryRings and Algebras16G20; 05E15text