epsilonBounds -- computes bounds for the Seshadri constant a general point

Synopsis

• Usage:

  epsilonBounds(P)

• Inputs:
  • P, a convex polyhedron, of dimension 2
  • n, an integer,
• Outputs:
  • L, a list, Containin bounds a and b such that a<=epsilon(X_P,L_P;1_P)<=b

Description

epsilonBounds is a function. It computes bounds for the Seshadri constant at a general point by applying a set of projections. The integer n determines which projections are considered.

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

i2 : Q=convexHull(matrix{{0,4}});

i3 : R=cayley({P,Q},2);

i4 : S=convexHull(matrix{{0,1,-1},{1,0,-1}});

i5 : epsilonBounds(R,10)

o5 = {2, 2}

o5 : List

i6 : epsilonBounds(S,10)

      3
o6 = {-, 2}
      2

o6 : List

See also

• isJetSpanned -- checks if the polarized toric variety associated to a set of lattice points is k-jet spanned at a given point.