This paper shows smooth non-projective complete toric threefolds improve to projective after flops, indicating geometry can change through specific transformations.
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.
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Fujino et al. (2025) studied this question.
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