Wall in the stability space of the gluing stability conditions on Hirzebruch surfaces

This paper investigates the wall structure of the space of stability conditions on Hirzebruch surfaces. Using the gluing construction of \cite{CP} and \cite{Uch} with respect to a fixed semiorthogonal decomposition, we focus on two main objectives: observing the intersection of the geometric chamber $U(S)\subset \mathrm{S}\mathrm{t}\mathrm{a}\mathrm{b}({\mathrm{\Sigma }}_e)$ with the walls of the resulting subspace, and determining the moduli space of $\sigma$-semistable objects on this subspace.