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Macaulay2 web site
NormalToricVarieties
::
Working with divisors and their associated groups
Working with divisors and their associated groups
The following methods allows one to make and manipulate torus-invariant Weil divisors on a normal toric variety.
Menu
toricDivisor(List,NormalToricVariety)
-- make a torus-invariant Weil divisor
toricDivisor(NormalToricVariety)
-- make the canonical divisor
NormalToricVariety _ ZZ
-- make a torus-invariant prime divisor
ToricDivisor
-- the class of all torus-invariant Weil divisors
expression(ToricDivisor)
-- get the expression used to format for printing
normalToricVariety(ToricDivisor)
-- get the underlying normal toric variety
support(ToricDivisor)
-- make the list of prime divisors with nonzero coefficients
vector(ToricDivisor)
-- make the vector of coefficients
ToricDivisor + ToricDivisor
-- arithmetic of 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
isAmple(ToricDivisor)
-- whether a torus-invariant Weil divisor is ample
isVeryAmple(ToricDivisor)
-- whether a torus-invariant Weil divisor is very ample
vertices(ToricDivisor)
-- computes the vertices of the associated polytope
latticePoints(ToricDivisor)
-- computes the lattice points in the associated polytope
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.
Menu
wDiv(NormalToricVariety)
-- make the group of torus-invariant Weil divisors
fromWDivToCl(NormalToricVariety)
-- get the map from Weil divisors to the class group
cl(NormalToricVariety)
-- make the class group
cDiv(NormalToricVariety)
-- make 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
pic(NormalToricVariety)
-- make the Picard group
fromPicToCl(NormalToricVariety)
-- get the map from Picard group to class group
See also
Making normal toric varieties
Basic invariants and properties of normal toric varieties
Total coordinate rings and coherent sheaves
Resolution of singularities