  We analyze properties of superconducting state (for both s-wave and d-wave
pairing), appearing on the "background" of the pseudogap state, induced by
fluctuations of "dielectric" (AFM(SDW) or CDW) short -- range order in the
model of the Fermi surface with "hot spots". We present microscopic derivation
of Ginzburg - Landau expansion, taking into account all Feynman diagrams of
perturbation theory over electron interaction with this short - range order
fluctuations, leading to strong electronic scattering in the vicinity of "hot
spots". We determine the dependence of superconducting critical temperature on
the effective width of the pseudogap and on correlation length of short - range
order fluctuations. We also find similar dependences of the main
characteristics of such superconductor close to transition temperature. It is
shown particularly, that specific heat discontinuity at the transition
temperature is significantly decreased in the pseudogap region of the phase
diagram.
