ALGEBRAIC POLYGONS

In this paper we prove the following: Over each algebraically closed f ield K of characteristic 0 there exist precisely three algebraic polyg ons (up to duality),namely the projective plane, the symplectic quadra ngle, and the split Cayley hexagon over K (Theorem 3.3). As a corollar y we prove that every algebraic Tits system over K is Moufang and obta in the following classification: THEOREM. Let (G,B,N,S) be an irreduci ble effective spherical Tits system of rank greater than or equal to 2 . If G is a connected algebraic group over an algebraically closed fie ld of characteristic 0, and if B is closed in G, then G is simple and B is a standard Borel subgroup of G. (C) 1996 Academic Press, Inc.