2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147123Using reduction to positive characteristic and the method of Frobenius splitting of diagonals, due to Mehta and Ramanathan, it is shown that homogeneous coordinate rings for either proper and smooth toric varieties or Schubert varieties are Koszul algebras.Revised version. Due to the mistake in alg-geom/9501012 the argument only works for homogeneous coordinate rings of Schubert varieties. This has also been proved by other authors and we have added references to themAlgebraic Geometrytext