working with divisors -- information about toric divisors and their related groups

The following methods allows one to make and manipulate torus-invariant Weil divisors on a normal toric variety.

Operations on toric divisors

• ToricDivisor -- the class of all torus-invariant Weil divisors
• toricDivisor(List,NormalToricVariety) -- make a torus-invariant Weil divisor
• toricDivisor(NormalToricVariety) -- make the canonical divisor
• toricDivisor(Polyhedron) -- make the toric divisor associated to a polyhedron
• smallAmpleToricDivisor(ZZ,ZZ) -- get a very ample toric divisor from the database
• NormalToricVariety _ ZZ -- make an irreducible torus-invariant divisor
• normalToricVariety(ToricDivisor) -- get the underlying normal toric variety
• expression(ToricDivisor) -- get the expression used to format for printing
• support(ToricDivisor) -- make the list of irreducible divisors with nonzero coefficients
• entries(ToricDivisor) -- get the list of coefficients
• ToricDivisor + ToricDivisor -- perform arithmetic on toric divisors
• OO ToricDivisor -- make the associated rank-one reflexive sheaf
• isEffective(ToricDivisor) -- whether a torus-invariant Weil divisor is effective
• isCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is Cartier
• isQQCartier(ToricDivisor) -- whether a torus-invariant Weil divisor is QQ-Cartier
• isNef(ToricDivisor) -- whether a torus-invariant Weil divisor is nef
• nefGenerators(NormalToricVariety) -- compute generators of the nef cone
• isAmple(ToricDivisor) -- whether a torus-invariant Weil divisor is ample
• isVeryAmple(ToricDivisor) -- whether a torus-invariant Weil divisor is very ample
• vertices(ToricDivisor) -- compute the vertices of the associated polytope
• latticePoints(ToricDivisor) -- compute the lattice points in the associated polytope
• monomials(ToricDivisor) -- list the monomials that span the linear series
• polytope(ToricDivisor) -- makes the associated 'Polyhedra' polyhedron

One can also work with the various groups arising from torus-invariant and the canonical maps between them.

Associated groups and maps

• weilDivisorGroup(NormalToricVariety) -- make the group of torus-invariant Weil divisors
• fromWDivToCl(NormalToricVariety) -- get the map from the group of Weil divisors to the class group
• classGroup(NormalToricVariety) -- make the class group
• cartierDivisorGroup(NormalToricVariety) -- compute the group of torus-invariant Cartier divisors
• fromCDivToWDiv(NormalToricVariety) -- get the map from Cartier divisors to Weil divisors
• fromCDivToPic(NormalToricVariety) -- get the map from Cartier divisors to the Picard group
• picardGroup(NormalToricVariety) -- make the Picard group
• fromPicToCl(NormalToricVariety) -- get the map from Picard group to class group