next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
MultiplierIdeals :: multiplierIdeal

multiplierIdeal -- multiplier ideal

Description

multiplier ideal of a monomial ideal

Computes the multiplier ideal of I with coefficient t using Howald's Theorem and the package Normaliz.
R = QQ[x,y];
I = monomialIdeal(y^2,x^3);
multiplierIdeal(I,5/6)
J = monomialIdeal(x^8,y^6); -- Example 2 of [Howald 2000]
multiplierIdeal(J,1)

multiplier ideal of a hyperplane arrangement

Computes the multiplier ideal of the ideal of A with coefficient s using the package HyperplaneArrangements.
R = QQ[x,y,z];
f = toList factor((x^2 - y^2)*(x^2 - z^2)*(y^2 - z^2)*z) / first;
A = arrangement f;
multiplierIdeal(A,3/7)

multiplier ideal of monomial space curve

Computes the multiplier ideal of the space curve C parametrized by (ta,tb,tc) given by n=(a,b,c).

R = QQ[x,y,z];
n = {2,3,4};
t = 5/2;
I = multiplierIdeal(R,n,t)

multiplier ideal of a generic determinantal ideal

  • Usage:
    multiplierIdeal(R,L,r,t)
  • Inputs:
    • R, a ring, a ring
    • L, a list, dimensions {m,n} of a matrix
    • r, an integer, the size of minors generating the determinantal ideal
    • t, a rational number, a coefficient
  • Outputs:
Computes the multiplier ideal of the ideal of r ×r minors in a m ×n matrix whose entries are independent variables in the ring R (a generic matrix).
x = symbol x;
R = QQ[x_1..x_20];
X = genericMatrix(R,4,5);
multiplierIdeal(X,2,5/7)

See also

Ways to use multiplierIdeal :