chap0.txt

  
  
                                     Toric 
  
  
          toric varieties and some combinatorial geometry computations 
  
  
                                     1.9.4
  
  
                                   07/03/2017
  
  
                                  David Joyner
  
  
  
  David Joyner
      Email:    mailto:[email protected]
      Homepage: https://sites.google.com/site/wdjoyner/
      Address:  W. David Joyner
                Mathematics Department
                U. S. Naval Academy
                Annapolis, MD 21402
                USA
  
  
  
  -------------------------------------------------------
  Copyright
  © 2004-2017 David Joyner.
  
  
  -------------------------------------------------------
  Acknowledgements
  The code for the toric package was written during the summer of 2002. It was
  put into GAP package format in the summer of 2004.
  
  toric  is  free software; you can redistribute it and/or modify it under the
  terms of the MIT License.
  
  toric  is  distributed  in  the hope that it will be useful, but WITHOUT ANY
  WARRANTY;  without  even  the implied warranty of MERCHANTABILITY or FITNESS
  FOR A PARTICULAR PURPOSE. See the MIT License for more details.
  
  This  documentation was prepared with the GAPDoc package of Frank Lübeck and
  Max  Neunhöffer. Moreover, a bug in toric 1.8 was fixed with the help of Max
  Horn,  and  this  documentation  was  modified accordingly. Finally, I thank
  Alexander  Konovalov  and  Max Horn for transferring this package to the new
  Git repository.
  
  
  -------------------------------------------------------
  
  
  Contents (toric)
  
  1 Introduction
    1.1 Introduction to the toric package
    1.2 Introduction to constructing toric varieties
      1.2-1 Generalities
      1.2-2 Basic combinatorial geometry constructions
      1.2-3 Basic affine toric variety constructions
      1.2-4 Riemann-Roch spaces and related constructions
  2 Cones and semigroups
    2.1 Cones
      2.1-1 InsideCone
      2.1-2 InDualCone
      2.1-3 PolytopeLatticePoints
      2.1-4 Faces
      2.1-5 ConesOfFan
      2.1-6 NumberOfConesOfFan
      2.1-7 ToricStar
    2.2 Semigroups
      2.2-1 DualSemigroupGenerators
  3 Affine toric varieties
    3.1 Ideals defining affine toric varieties
      3.1-1 EmbeddingAffineToricVariety
  4 Toric varieties X(∆)
    4.1 Riemann-Roch spaces
      4.1-1 DivisorPolytope
      4.1-2 DivisorPolytopeLatticePoints
      4.1-3 RiemannRochBasis
    4.2 Topological invariants
      4.2-1 EulerCharacteristic
      4.2-2 BettiNumberToric
    4.3 Points over a finite field
      4.3-1 CardinalityOfToricVariety