2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62490A necessary condition for the existence of torus-equivariant crepant resolutions of Gorenstein toric singularities can be derived by making use of a variant of the classical Upper Bound Theorem which is valid for simplicial balls.Latex 2e, 6 pages. To appear in ``Géométrie des variétés toriques'', (Proc. of SS 2000, Grenoble), collection S'eminaires et Congr`es, SMF 2002. A preliminary version of these proceedings is available http://www-fourier.ujf-grenoble.fr/~mbrion/ecole.htmlAlgebraic GeometryCombinatoricsPrimary 14M25, 52B20; Secondary 14B05, 52B05, 52B11text