2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222623We study local automorphisms of holomorphic Cartan geometries. This leads to classification results for compact complex manifolds admitting Cartan geometries. We prove that a compact Calabi-Yau manifold bearing a holomorphic Cartan geometry of algebraic type admits a finite unramified cover which is a complex torus.10 pages; the main result was improved; corrected typosDifferential GeometryAlgebraic Geometry53B21; 53C56; 53A55text