On the classification of toric fano varieties

@article{Ewald1988OnTC,
  title={On the classification of toric fano varieties},
  author={G{\"u}nter Ewald},
  journal={Discrete \& Computational Geometry},
  year={1988},
  volume={3},
  pages={49-54}
}
  • G. Ewald
  • Published 1 December 1988
  • Mathematics, Computer Science
  • Discrete & Computational Geometry
Toric Fano varieties are algebraic varieties associated with a special class of convex polytopes inR′'. We extend results of V. E. Voskresenskij and A. A. Klyachko about the classification of such varieties using a purely combinatorial method of proof. 

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References

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TOROIDAL FANO VARIETIES AND ROOT SYSTEMS
In this paper it is shown that over an algebraically closed field there exist only finitely many mutually nonisomorphic toroidal Fano varieties. We give a complete description of toroidal Fano
Spherical complexes and nonprojective toric varieties
  • G. Ewald
  • Mathematics, Computer Science
    Discret. Comput. Geom.
  • 1986
A combinatorial criterion for a toric variety to be projective is given which uses Gale-transforms. Furthermore, classes of nonprojective toric varieties are constructed.
THE GEOMETRY OF TORIC VARIETIES
ContentsIntroductionChapter I. Affine toric varieties § 1. Cones, lattices, and semigroups § 2. The definition of an affine toric variety § 3. Properties of toric varieties § 4. Differential forms on