documentation:latest:fulton:tdivisor

Available versions of this document: latest release, release 4.0, release 3.6, release 3.5, nightly master

Reference documentation for older polymake versions: release 3.4, release 3.3, release 3.2

BigObject TDivisor

from application fulton

A T-invariant divisor on a normal toric variety.

Properties from algebraic geometry.

AMPLE

True if the divisor is ample.

Type:
Bool

BASEPOINT_FREE

True if the divisor is basepoint-free.

Type:
Bool

CARTIER

True if the divisor is Cartier.

Type:
Bool

EFFECTIVE

True if the divisor is effective.

Type:
Bool

INTEGRAL

True if the divisor is integral.

Type:
Bool

NEF

True if the divisor is nef.

Type:
Bool

PRINCIPAL

True if the divisor is principal.

Type:
Bool

Q_CARTIER

A divisor is Q-Cartier if some multiple of it is CARTIER.

Type:
Bool

SEMIAMPLE

True if the divisor is semiample.

Type:
Bool

VERY_AMPLE

True if the divisor is very ample.

Type:
Bool

These properties capture combinatorial information of the object. Combinatorial properties only depend on combinatorial data of the object like, e.g., the face lattice.

CARTIER_DATA

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

Type:
Map<Set<Int>,Vector<Rational>>

COEFFICIENTS

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.

Type:
Vector<Rational>

SECTION_POLYTOPE

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

Type:
Polytope<Rational>

• documentation/latest/fulton/tdivisor.txt