Toric_Varieties_and_Related

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title: Toric Varieties and Related permalink: wiki/Toric_Varieties_and_Related/ layout: wiki

Things to add or change in NormalToricVarieties.m2

• Add a strategy option to makeSimplicial that allows one to make it simplicial without adding rays(René)
• Add a function to insert a cone into the fan of a NormalToricVariety. This cone should be given by a set of rays and must be contained in one of the cones of the fan(René)
• Add a function isOrbifold
• Add functions is Fano, isCartier, isQQCartier, isAmple, isVeryAmple (René), isSemiprojective
• Import all functions from ToricResolve.m2 into NormalToricVarieties.m2 (Alexandra)
• Add new option to makeSmooth and resolve which picks a ray of maximum order with respect to the quotient group of the ambient lattice mod the lattice spanned by the rays of a cone (Alexandra)
• Documentation needed for
  • halfspaces, (René)
  • hyperplanes, (René)
  • stellarSubdivision, (Alexandra)
  • fan, (René)
  • isComplete, (Alexandra)
  • isPure, (Alexandra)
  • insertCone, (René)
  • normalToricVariety(Polyhedron/Fan), (René)
  • isFano, (René)
  • isCartier, (René)
  • isQQCartier, (René)
  • isAmple, (René)
  • isVeryAmple (René)
  • polytope(divisor(List),NTV) (René)
  • polytope NTV (René)
  • makeSimplicial (Alexandra)
  • isProjective (René)
  • examples for dim(Cone,NTV)(Alexandra)
• Add a function that takes a polytope and returns the normal toric variety of the normal fan and the given divisor

Divisors on NormalToricVarieties

• Create a new type ToricDivisor. This should be a hashTable with keys coefficients,variety,cache (René)
• Make all existing functions that consider divisors given by just a list access ToricDivisor s (René)