Fano manifolds whose elementary contractions are smooth P^1-fibrations: a geometric characterization of flag varieties

Abstract

The present paper provides a geometric characterization of complete flag varieties for semisimple algebraic groups.Namely, if X is a Fano manifold whose all elementary contractions are P 1 -fibrations then X is isomorphic to the complete flag manifold G/B where G is a semi-simple Lie algebraic group and B is a Borel subgroup of G.