2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/137240We give an algebraic construction of the positive products of pseudo-effective classes first introduced by Boucksom, Demailly, Paun and Peternell, and use them to prove that the volume function on the Neron-Severi space of a projective variety is (once) differentiable. The differential is expressed as a positive product; we also relate it to the restricted volumes introduced by Ein et al and by Takayama. Then we apply our differentiability result to prove an algebro-geometric version of the Diskant inequality in convex geometry, allowing us to characterize the equality case of the Khovanskii-Teissier inequalities for nef and big classes.28 pages. Final version. To appear in J. Alg. GeomAlgebraic Geometry14C20 (Primary); 14E05, 52A40 (Secondary)text