In his comments to the Upadesa Sutras (1.2.1), Ernst writes that: « When amsa is used in an isolated sense without a number in front of it, it refers to the navamsa, the 9th division. Svamsa therefore refers to something in the navamsa and this something represents the self. ».
The self is the atmakaraka.
So, the svamsa is the sign in the D9 where the atmakaraka is placed.
In my opinion, the notion of "svamsa" is only attached to the D9. If we want to use this technique in another varga, we have to apply the same rule: find the sign where the atmakaraka falls in such varga and read from that sign.
In all the answers Ernst gives in the homeworks for the Upadesa Sutras 1, when dealing with other vargas than the D9, Ernst applies the Jaimini rules from the position of the Atmakaraka in such varga and not from the position of the sign where the atmakaraka falls in the D9 (=svamsa).
I hope this helps.
Olivier
For the sake of discussion, I certainly agree that the Svamsa is the sign in the D9 where the atmakaraka is placed. At the same time, we are defining the Svamsa as a rasi sign. These rasi signs exist in all vargas. In this regard, I'm unclear on what basis you are asserting that "the notion of "svamsa" is only attached to the D9." Certainly, the rasi sign is determined in the D9 as given.
Ernst writes, "If one wants to study the native it is the Navamsa of the Atma Karaka. If one wants to study the spouse it is the Navamsa of the Dara Karaka. The term Svamsa, when used alone, represents the Navamsa of the Atma Karaka. If one wants to study the spouse it is the Navamsa of the Dara Karaka. The term Svamsa, when used alone, represents the Navamsa of the Atma Karaka, while the Svamsa of the spouse would be called the Svamsa of the Dara Karaka, or the spouses Svamsa." All of these designations are rasi signs.
I agree that Ernst focused many lessons around reading from the AK in many vargas with illuminating examples. I would however, argue that the seven different "svamsas" are defined as rasi signs. I do not believe that Jaimini wanted us to confuse the concept of "svamsa" with karakas, nor limit us to a single varga. I am merely attempting to point out the distinction between two different things. This is something for further research. Maybe Ernst will get into these matters more deeply in a Jaimini 2.0 class.
John