Representation of the number n/q as a Hirzebruch-Jung continued fraction. Take care that this property agrees with the dual property.

Representation of the number n/(n-q) as a Hirzebruch-Jung continued fraction. Take care that this property agrees with the dual property.

Every cyclic quotient variety corresponds to a cone given by the rays (1,0) and (-q,n).

Every cyclic quotient variety corresponds to a cone given by the rays (1,0) and (-q,n).

Evaluates true if the toric variety is affine, i.e. the fan consists of a single cone.

Polytope such that the fan of the toric variety is the normal fan of this polytope. This does not necessarily exist. For determining existence and computation we use Shepards theorem.

Evaluates to true if the corresponding fan is the normal fan of some polytope. Alias for property REGULAR.

a toric variety is DEGENERATE if the fan is not FULL_DIM

The cone of effective divisors in the rational class group A class of divisors D is effective if the corresponding polytope P_D is non-empty

a toric variety is FANO if the anticanonical divisor is AMPLE true if the toric variety is a Fano variety

The dual of the NEF_CONE

The cone of nef divisors in the rational class group this is the closure of the cone of ample divisors, where a divisor of the variety is ample if the fan coincides with the normal fan of P_D equivalently, a divisor is nef if the inequalities it defines are tight on P_D

the number of maximal torus orbits. Equals the number of rays of the fan

a toric variety is an ORBIFOLD if the fan is SIMPLICIAL

the torsion free part of the class group

a toric variety is SMOOTH if the fan is PolyhedralFan::SMOOTH Alias for property SMOOTH_FAN.

a toric invariant divisor on the variety given by the fan it is represented by n integer vector with entries corresponding to the rays of the fan the actual divisor is stored in the property COEFFICIENTS

lifts a divisor in the class group onto a divisor on the fan

maps a divisor on the variety onto its representation in the class group

true if the divisor is ample

true if the divisor is basepoint-free

true if the divisor is Cartier

contains the Cartier data of the divisor, if it is Cartier i.e. contains a list of vertices of the lattice polytope P defined by the divisor and the variety the vertices appear in the same order as the maximal cones of the fan

The divisor on a toric variety, given as a list of coefficients for the torus invariant divisors corresponding to the RAYS of the fan. Take care of labeling of the Rays.

true if the divisor is effective

true if the divisor is integral

true if the divisor is nef

true if the divisor is principal

true if the divisor is Q-Cartier, i.e. some multiple of it is Cartier

The polytope whose lattice points correspond to the global sections of the divisor.

true if the divisor is semiample