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Toric 2-Fano manifolds and extremal contractions. (English) Zbl 1375.14177

Summary: 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.

MSC:

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14J45 Fano varieties
14E30 Minimal model program (Mori theory, extremal rays)
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