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NormalToricVarieties -- working with normal toric varieties and related objects


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, improved existing code, or enhanced the documentation: Paul Aspinwall, Christine Berkesch, René Birkner, Justin Chen, Chris Eur, Matthew Faust, Corey Harris, Michael Loper, Diane Maclagan, Maryam Nowroozi, Erika Pirnes, Ritvik Ramkumar, Julie Rana, Mahrud Sayrafi, Alexandra Seceleanu, Mike Stillman, Sameera Vemulapalli, Elise Walker, Weikun Wang, Rachel Webb, Thomas Yahl, and Jay Yang.

See also



This documentation describes version 1.9 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/.


For the programmer

The object NormalToricVarieties is a package.