Smooth projective toric varieties whose nontrivial nef line bundles are big. (English) Zbl 1189.14056

Fujino, Osamu; Sato, Hiroshi

Proc. Japan Acad., Ser. A 85, No. 7, 89-94 (2009).

For every \(k \geq 5\), the authors construct a smooth projective toric threefold of Picard number \(k\) on which every nontrivial nef line bundle is big. These examples complement the work of the author and S. Payne [Proc. Japan Acad., Ser. A 81, No. 10, 174-179 (2005; Zbl 1141.14313)], where complete (non-projective) toric threefolds without nontrivial nef line bundles were described. The toric varieties in question are obtained by suitably blowing up \(\mathbb{P}^3\).

Reviewer: Christian Schnell (Chicago)

MSC:

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

Keywords:

toric variety; Mori theory; nef cone; pseudo-effective cone

Citations:

Zbl 1141.14313

References:

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