2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213794The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the authors have found a far-reaching generalization of this theorem to generic systems of algebraic equations on any quasi-projective variety. In the present note we review these results and their applications to algebraic geometry and convex geometry.16 pages. To appear in the conference volume in honor of Oleg Y. ViroAlgebraic Geometry14C20; 52A39text