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We obtain an algebro-geometric proof of the surjectivity of the multiplication map of complete linear systems of ample divisor and nef divisor on a nonsingular projective toric surface. As a consequence, we show that on a nonsingular toric Fano 3-fold, the multiplication map of complete linear systems of the anti-canonical divisor and a nef divisor is surjective.

Multiplication Maps of Complete Linear Systems on Projective Toric Surfaces