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There are well known examples of smooth (hence simplicial) complete toric varieties which are not projective,. See for example in Chapter 3p. 71 of Fulton's bookIntroduction to Toric Varieties. Any such variety gives a counterexample.
There are well known examples of smooth (hence simplicial) toric varieties which are not projective, for example in Chapter 3 of Fulton's book. Any such variety gives a counterexample.
There are well known examples of smooth (hence simplicial) complete toric varieties which are not projective. See for example p. 71 of Fulton's bookIntroduction to Toric Varieties. Any such variety gives a counterexample.
There are well known examples of smooth (hence simplicial) toric varieties which are not projective, for example in Chapter 3 of Fulton's book. Any such variety gives a counterexample.