# THE FUNCTOR OF A SMOOTH TORIC VARIETY

@article{Cox1993THEFO, title={THE FUNCTOR OF A SMOOTH TORIC VARIETY}, author={David A. Cox}, journal={Tohoku Mathematical Journal}, year={1993}, volume={47}, pages={251-262} }

(1) Y 7→ {line bundle quotients of O Y } . This is easy to prove since a surjection O Y → L gives n + 1 sections of L which don’t vanish simultaneously and hence determine a map Y → Pnk . The goal of this paper is to generalize this representation to the case of an arbitrary smooth toric variety. We will work with schemes over an algebraically closed field k of characteristic zero, and we will fix a smooth n-dimensional toric variety X determined by the fan ∆ in NR = R. As usual, M denotes the… Expand

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