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}
}
  • D. Cox
  • Published 3 December 1993
  • Mathematics
  • Tohoku Mathematical Journal
(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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This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each one-dimensional cone in the fan ∆ determining X, and S hasExpand
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Let $X$ be a compact toric variety. Let $Hol$ denote the space of based holomorphic maps from $CP^1$ to $X$ which lie in a fixed homotopy class. Let $Map$ denote the corresponding space of continuousExpand
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