On Simplicial Toric Varieties Which Are Set-Theoretic Complete Intersections

In this paper we prove: • In characteristic > 0 every simplicial toric affine or projective variety with full parametrization is a set-theoretic complete intersection. This extends previous results by R. Hartshorne (1979, , 380–383) and T. T. Moh (1985, , 217–220). • In any characteristic, every simplicial toric affine or projective variety with full parametrization is an almost set-theoretic complete intersection. This extends previous known results by M. Barile and M. Morales (1998, , 1907–1912) and A. Thoma (, to appear). • In any characteristic, every simplicial toric affine or projective variety of codimension two is an almost set-theoretic complete intersection. Moreover the proofs are constructive and the equations we find are binomial ones.