Available versions of this document: latest release, 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.

Algebraic Geometry

Properties from algebraic geometry.


AMPLE

True if the divisor is ample.

Type:

BASEPOINT_FREE

True if the divisor is basepoint-free.

Type:

CARTIER

True if the divisor is Cartier.

Type:

EFFECTIVE

True if the divisor is effective.

Type:

INTEGRAL

True if the divisor is integral.

Type:

NEF

True if the divisor is nef.

Type:

PRINCIPAL

True if the divisor is principal.

Type:

Q_CARTIER

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

Type:

SEMIAMPLE

True if the divisor is semiample.

Type:

Combinatorics

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:

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:

SECTION_POLYTOPE

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

Type:

  • documentation/latest/fulton/tdivisor.txt
  • Last modified: 2019/08/13 10:31
  • (external edit)