Toric 2-Fano manifolds and extremal contractions

Abstract

We show that for a projective toric manifold with the ample second Chern character, if there exists a Fano contraction, then it is isomorphic to the projective space. For the case that the second Chern character is nef, the Fano contraction gives either a projective line bundle structure or a direct product structure. We also show that, for a toric weakly 2-Fano manifold, there does not exist a divisorial contraction to a point.