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logCanonicalThreshold(CentralArrangement) -- compute the log-canonical threshold of an arrangement

Synopsis

Function: logCanonicalThreshold
Usage:

logCanonicalThreshold(A)

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]

o1 = R

o1 : PolynomialRing

i2 : A = arrangement ((x^2 - y^2)*(x^2 - z^2)*(y^2 - z^2)*z)

o2 = {z, y - z, y + z, x - z, x + z, x - y, x + y}

o2 : Hyperplane Arrangement

i3 : logCanonicalThreshold A

     3
o3 = -
     7

o3 : QQ

Note that $A$ is allowed to be a multiarrangement.

See also

multiplierIdeal -- compute a multiplier ideal

Ways to use this method:

logCanonicalThreshold(CentralArrangement) -- compute the log-canonical threshold of an arrangement