  
  
                                    [1X Toric [101X
  
  
         [1X toric varieties and some combinatorial geometry computations [101X
  
  
                                     1.9.4
  
  
                                   07/03/2017
  
  
                                  David Joyner
  
  
  
  David Joyner
      Email:    [7Xmailto:wdjoyner@gmail.com[107X
      Homepage: [7Xhttps://sites.google.com/site/wdjoyner/[107X
      Address:  [33X[0;14YW. David Joyner[133X
                [33X[0;14YMathematics Department[133X
                [33X[0;14YU. S. Naval Academy[133X
                [33X[0;14YAnnapolis, MD 21402[133X
                [33X[0;14YUSA[133X
  
  
  
  -------------------------------------------------------
  [1XCopyright[101X
  [33X[0;0Y© 2004-2017 David Joyner.[133X
  
  
  -------------------------------------------------------
  [1XAcknowledgements[101X
  [33X[0;0YThe code for the [5Xtoric[105X package was written during the summer of 2002. It was
  put into [5XGAP[105X package format in the summer of 2004.[133X
  
  [33X[0;0Y[5Xtoric[105X  is  free software; you can redistribute it and/or modify it under the
  terms of the MIT License.[133X
  
  [33X[0;0Y[5Xtoric[105X  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.[133X
  
  [33X[0;0YThis  documentation was prepared with the [5XGAPDoc[105X 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.[133X
  
  
  -------------------------------------------------------
  
  
  [1XContents (toric)[101X
  
  1 [33X[0;0YIntroduction[133X
    1.1 [33X[0;0YIntroduction to the [5Xtoric[105X package[133X
    1.2 [33X[0;0YIntroduction to constructing toric varieties[133X
      1.2-1 [33X[0;0YGeneralities[133X
      1.2-2 [33X[0;0YBasic combinatorial geometry constructions[133X
      1.2-3 [33X[0;0YBasic affine toric variety constructions[133X
      1.2-4 [33X[0;0YRiemann-Roch spaces and related constructions[133X
  2 [33X[0;0YCones and semigroups[133X
    2.1 [33X[0;0YCones[133X
      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 [33X[0;0YSemigroups[133X
      2.2-1 DualSemigroupGenerators
  3 [33X[0;0YAffine toric varieties[133X
    3.1 [33X[0;0YIdeals defining affine toric varieties[133X
      3.1-1 EmbeddingAffineToricVariety
  4 [33X[0;0YToric varieties [22XX(∆)[122X[133X
    4.1 [33X[0;0YRiemann-Roch spaces[133X
      4.1-1 DivisorPolytope
      4.1-2 DivisorPolytopeLatticePoints
      4.1-3 RiemannRochBasis
    4.2 [33X[0;0YTopological invariants[133X
      4.2-1 EulerCharacteristic
      4.2-2 BettiNumberToric
    4.3 [33X[0;0YPoints over a finite field[133X
      4.3-1 CardinalityOfToricVariety
  
  
  [32X
