2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148625Recently proposed scenarios for the cuprates make extensive use of a ``flat'' quasiparticle (q.p.) dispersion and short-range hole-hole interactions in real-space, both caused by antiferromagnetic (AF) correlations. The density of states (DOS) at half-filling has a robust peak which boosts the superconducting critical temperature $T_c$ to large values as holes are introduced into the (rigid) q.p. band. Here, the stability of such scenarios is studied after a $finite$ but small hole density is introduced. The overall conclusion is that the main features of real-space AF-based approaches remain qualitatively similar, namely a large $T_c$ is found and superconductivity (SC) appears in the ${\rm d_{x^2 - y^2}}$ channel. As the hole density grows the chemical potential $μ$ crosses a broad peak in the DOS. We also observe that extended s-wave SC competes with d-wave in the overdoped regime.RevTeX (version 3.0), 5 twocolumn pages with 3 embedded figures, added referencesCondensed Mattertext