Toric Varieties and Related

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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)