Meaning of stable $CP^2$

Question

I came across the following phrase in arXiv:1903.08904

....in order to have a stable $CP^2$ , i.e., one in which all the automorphism group is fixed...

Can anyone explain to me what one means by a stable $CP^2$? It is mentioned in the phrase itself, but I do not know what one means by a fixed automorphism group. It must be some usual mathematical terminology which I am not aware of, so please help.

Answer 1

Stability normally refers to stability under some action. Given some homomorphism $T: \text{End}(\mathbb{C}P^2) \to \text{End}(\mathbb{C}P^2)$, we would say that $\text{Aut}(\mathbb{C}P^2)$ is stable under $T$ (or $T$-stable) if $T: \text{Aut}(\mathbb{C}P^2) \to \text{Aut}(\mathbb{C}P^2)$.