Multiplication maps of linear systems on smooth projective toric surfaces

Abstract

Let X be a smooth projective toric surface and L and M two line bundles on X. If L is ample and M is generated by global sections, then we show that the natural map from H^0(X,L) tensor H^0(X,M) to H^0(X, L tensor M) is surjective. We also consider a generalization to the case when M is an arbitrary line bundle with h^0(X,M) > 0.

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Cited by in corpus (5)

• Syzygies, multigraded regularity and toric varieties
• Lattice points in Minkowski sums
• Positivity for toric vector bundles
• Integer decomposition property of polytopes
• Unimodular covers of 3-dimensional parallelepipeds and Cayley sums