On non-projective complete toric varieties

Abstract

For every complete toric variety, there exists a projective toric variety which is isomorphic to it in codimension one. In this paper, we show that every smooth non-projective complete toric threefold of Picard number at most five becomes projective after a finite succession of flops or anti-flips.

24 pages, v2: revisions following referee's comments and suggestions, to appear in Exp. Math