2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/156496We give a partial positive answer to a conjecture of Tyurin (\cite {Tyu}). Indeed we prove that on a general quintic hypersurface of $\Pj^4$ every arithmetically Cohen--Macaulay rank 2 vector bundle is infinitesimally rigid.Algebraic Geometry14F05text