  We study the half filled Hubbard chain including next-nearest-neighbor
hopping $t'$. The model has three phases: one insulating phase with dominant
spin-density-wave correlations at large distances (SDWI), another phase with
dominant spin-dimer correlations or dimerized insulator (DI), and a third one
in which long distance correlations indicate singlet superconductivity (SS).
The boundaries of the SDWI are accurately determined numerically through a
crossing of excited energy levels equivalent to the jump in the spin Berry
phase. The DI-SS boundary is studied using several indicators like correlation
exponent $K_{\rho}$, Drude weight $D_{c}$, localization parameter $z_{L}$ and
charge gap $\Delta_{c}$.
