Symplectic 4-manifolds on the Noether line and between the Noether and half Noether lines

We construct simply connected, minimal, symplectic 4-manifolds with exotic smooth structures and each one Seiberg–Witten basic class up to sign, on the Noether line between half lines by star surgeries introduced Karakurt Starkston, using complex singularities. also certain configurations of singularities in rational elliptic surfaces geometrically, without any monodromy arguments. By these configurations, we give embeddings shaped plumbings inside (some blow-ups of) surfaces.