what curved is assumed when kg is zero and kn is being righting lever measured from the keel.

The curve assumed is the stability cross curve, specifically the KN curve. When KG is taken as zero , the righting lever is measured from the keel, so the plotted curve is KN , and the actual righting lever is then found by GZ = KN - KG \sin \theta.

In plain words

• KG is the height of the ship’s center of gravity above the keel.
• KN is the righting lever referenced from the keel.
• If KG = 0 , the curve itself gives the lever directly from the keel, which is why it is called a KN curve.

Why this is done

Using KG = 0 avoids mixing in the ship’s actual center-of-gravity position while building the curve, so the same curve can be used later for different loading conditions by applying the correction KG sin θ.

If you want, I can also explain the difference between GZ , KN , and KM in one simple sketch-style explanation.