# 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, ,
• Q, ,
• M, ,
• N, ,
• k, an integer,
• Outputs:

## 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 .