PT1 -- Compute the deformation polytope associated to a Stanley-Reisner complex.

Synopsis

• Usage:
PT1(C)
• Inputs:
• C, ,
• Optional inputs:
• file => ..., default value null, Store result of a computation in a file.
• Outputs:
• ,

Description

Compute the deformation polytope of C, i.e., the convex hull of all homogeneous (i.e., degree(FirstOrderDeformation) zero) deformations associated to C, considering them as lattice monomials (i.e., their preimages under C.grading).

 i1 : R=QQ[x_0..x_3] o1 = R o1 : PolynomialRing i2 : I=ideal(x_0*x_1,x_2*x_3) o2 = ideal (x x , x x ) 0 1 2 3 o2 : Ideal of R i3 : C=idealToComplex I o3 = 1: x x x x x x x x 0 2 1 2 0 3 1 3 o3 : complex of dim 1 embedded in dim 3 (printing facets) equidimensional, simplicial, F-vector {1, 4, 4, 0, 0}, Euler = -1 i4 : PT1C=PT1 C o4 = 3: y y y y y y y y 0 1 2 3 4 5 6 7 o4 : complex of dim 3 embedded in dim 3 (printing facets) equidimensional, non-simplicial, F-vector {1, 8, 14, 8, 1}, Euler = 0

Caveat

To homogenize the denominators of deformations (which are supported inside the link) we use globalSections to deal with the toric case. The speed of this should be improved. For ordinary projective space homogenization with support on F is done much faster.