toricBlowUp -- calculates the stellar subdivision of a polytope at a given face.

Synopsis

Usage:

toricBlowUp(P,Q),

toricBlowUp(P,Q,k),

toricBlowUp(M,N),

toricBlowUp(M,N,k)
Inputs:
- P, a convex polyhedron,
- Q, a convex polyhedron,
- M, a matrix,
- N, a matrix,
- k, an integer,
Outputs:
- a convex polyhedron,

Description

Calculates the stellar subdivision of height k of a polytope P at the face Q. This corresponds to constructing the embedding given by the global sections of L-kE for the blow-up at the torus invariant subvariety associated to Q. Here L is the ample line bundle on the toric variety corresponding to P and E is the exceptional divisor.

i1 : P=cayley(matrix{{0,2,0}},matrix{{0,0,2}})

o1 = P

o1 : Polyhedron

i2 : vertices oo

o2 = | 0 2 0 2 |
     | 0 0 1 1 |

              2       4
o2 : Matrix QQ  <-- QQ

i3 : Q=convexHull(matrix{(vertices P)_0})

o3 = Q

o3 : Polyhedron

i4 : toricBlowUp(P,Q,1)
Warning: This method is deprecated and will be removed in version 1.11 of Polyhedra. Please consider using polyhedronFromHData instead.

o4 = Polyhedron{...1...}

o4 : Polyhedron

i5 : vertices oo

o5 = | 1 2 0 2 |
     | 0 0 1 1 |

              2       4
o5 : Matrix QQ  <-- QQ

Ways to use toricBlowUp :

toricBlowUp(Matrix,Matrix)
toricBlowUp(Matrix,Matrix,ZZ)
toricBlowUp(Polyhedron,Polyhedron)
toricBlowUp(Polyhedron,Polyhedron,ZZ)

For the programmer

The object toricBlowUp is a method function.