Acoustic plasmons and high-T-c superconductivity of cuprates with extendedsaddle point singularity in electron spectrum

It is shown that the strong anisotropy of the one-particle electron spectru m, due to the existence of extended saddle-point singularities close to the Fermi level in the hole-type cuprates, leads to the appearance of a low-fr equency peak in the spectral function of the charge density fluctuations du e to the presence of an acoustic plasmon branch in the collective electron spectrum. We argue that the retarded anisotropic electron-plasmon interacti on suppresses the static screened Coulomb repulsion for small transferred m omenta and provides the effective attraction between electrons in the d(x2- y2)-wave channel of the Cooper pairing of current carriers.