quasiToricManifold -- create a quasitoric manifold

Usage:

quasiToricManifold(K,lambda)
Inputs:
- K, an abstract simplicial complex,
- lambda, a matrix,
Outputs:
- a quasitoric manifold,

Description

Create a quasitoric manifold over K with characteristic matrix lambda. If lambda is not characteristic for K, an error is returned.

The following example creates the 2-dimensional complex projective space as a quasitoric manifold.

i1 : needsPackage "SimplicialComplexes"

o1 = SimplicialComplexes

o1 : Package

i2 : R = QQ[a..c]

o2 = R

o2 : PolynomialRing

i3 : K = simplicialComplex {a*b, b*c, c*a}

o3 = simplicialComplex | bc ac ab |

o3 : SimplicialComplex

i4 : lambda = matrix{{1, 0, -1}, {0, 1, -1}}

o4 = | 1 0 -1 |
     | 0 1 -1 |

              2       3
o4 : Matrix ZZ  <-- ZZ

i5 : X = quasiToricManifold(K, lambda)

o5 = QuasiToricManifold{QTMCharacteristicMatrix => | 1 0 -1 |                 }
                                                   | 0 1 -1 |
                        QTMDimension => 4
                        QTMSimplicialComplex => simplicialComplex | bc ac ab |

o5 : QuasiToricManifold

For the programmer

The object quasiToricManifold is a method function.

The source of this document is in ToricTopology.m2:540:0.