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HyperplaneArrangements :: lct

lct -- Compute the log-canonical threshold of an arrangement

Synopsis

Usage:
lct(A)
Inputs:
- A, a central hyperplane arrangement, a central hyperplane arrangement
Outputs:
- a rational number, The log-canonical threshold of A.

Description

The log-canonical threshold of A defined by a polynomial f is the least number c for which the multiplier ideal J(f^c) is nontrivial.

Let's consider Example 6.3 of Berkesch and Leykin from arXiv:1002.1475v2:

i1 : R := QQ[x,y,z];

i2 : f := toList factor((x^2 - y^2)*(x^2 - z^2)*(y^2 - z^2)*z) / first;

i3 : A := arrangement f

o3 = {z, y - z, y + z, x - z, x + z, x - y, x + y}

o3 : Hyperplane Arrangement

i4 : lct A

     3
o4 = -
     7

o4 : QQ

note that A is allowed to be a multiarrangement.

See also

multIdeal -- compute a multiplier ideal

Ways to use `lct` :

lct(CentralArrangement)