isStable -- determines whether the mth Hilbert point of I is GIT stable

Synopsis

• Usage:
isStable(3,I)
• Inputs:
• an integer, specifies which Hilbert point to test
• an ideal, the ideal

Description

Bayer and Morrison showed that GIT stability of the mth Hilbert point of I with respect to the maximal torus acting on a polynomial ring by scaling the variables can be tested by whether Statem(I) contains a certain point.
 i1 : R = QQ[a..d]; i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2); o2 : Ideal of R i3 : isStable(3,I) o3 = true i4 : I = ideal(a^2,b^2,b*c); o4 : Ideal of R i5 : isStable(3,I) o5 = false

Ways to use isStable :

• "isStable(ZZ,Ideal)"

For the programmer

The object isStable is .