A Counter-example To Fujino’s Conjecture On Complete Smooth Toric Varieties

The classification of complete smooth toric varities is an important problem in algebraic geometry.The smallest complete smooth non-projective toric variety was discovered by Oda,and there have been some results for small picard numbers of complete smooth non-projective toric varieties[10].In 2005,Fujino conjectured that every complete,smooth toric varity has a nontrivial nef line bundle[15],Payne presented a conuterexample of picard number 11.In this paper,we give an example of complete smooth non-projective toric variety with picard number 104.