2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66530This paper contains a new proof of the classification of elements of prime order in the Cremona group Bir(P^2), up to conjugation. In addition, we give explicit geometric constructions of these Cremona transformations, and provide a parameterization of their conjugacy classes. Analogous constructions in higher dimensions are also discussed.21 pages; AMS-LaTeX; v2: proofs of Proposition 4.3.2 (now 4.3.1) and Lemma 4.4.1 semplified, and few other minor changes, following referee's comments; one reference addedAlgebraic GeometryCommutative Algebra14E07,14J50(Primary);14E20(Secondary)text