2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59155We characterize embeddability of algebraic varieties into smooth toric varieties and prevarieties. Our embedding results hold also in an equivariant context and thus generalize a well known embedding theorem of Sumihiro on quasiprojective G-varieties. The main idea is to reduce the embedding problem to the affine case. This is done by constructing equivariant affine conoids, a tool which extends the concept of an equivariant affine cone over a projective G-variety to a more general framework.minor changes, to appear in Can. J. Math., 15 pagesAlgebraic Geometry14C20;14E25;14L30;14M25text