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NormalToricVarieties :: NormalToricVarieties

NormalToricVarieties -- package for working with normal toric varieties


A toric variety is an integral scheme such that an algebraic torus forms a Zariski open subscheme and the natural action this torus on itself extends to an action on the entire scheme. Normal toric varieties correspond to strongly convex rational polyhedral fans. This makes the theory of normal toric varieties very explicit and computable.

This Macaulay2 package is designed to manipulate normal toric varieties and related geometric objects. An introduction to the theory of normal toric varieties can be found in the following textbooks:

  • David A. Cox, John B. Little, Hal Schenck, Toric varieties, Graduate Studies in Mathematics 124. American Mathematical Society, Providence RI, 2011. ISBN: 978-0-8218-4817-7
  • Günter Ewald, Combinatorial convexity and algebraic geometry, Graduate Texts in Mathematics 168. Springer-Verlag, New York, 1996. ISBN: 0-387-94755-8
  • William Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, Princeton University Press, Princeton, NJ, 1993. ISBN: 0-691-00049-2
  • Tadao Oda, Convex bodies and algebraic geometry, an introduction to the theory of toric varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 15, Springer-Verlag, Berlin, 1988. ISBN: 3-540-17600-4


The following people have generously contributed code or worked on our code.




This documentation describes version 1.5 of NormalToricVarieties.

Source code

The source code from which this documentation is derived is in the file NormalToricVarieties.m2. The auxiliary files accompanying it are in the directory NormalToricVarieties/.