Although the cold + hot dark matter (CHDM) cosmology provides perhaps the best fit of any model to all the available data at the current epoch (z = 0), CHDM produces structure at relatively low redshifts and thus is very sensitive to the observed numbers of massive objects at high redshifts. Damped Lyα systems are abundant in quasar absorption spectra and provide possibly the most significant evidence for early structure formation, and thus a stringent constraint on CHDM. Using the numbers of halos in N-body simulations to normalize Press-Schechter estimates of the number densities of protogalaxies as a function of redshift, we find that CHDM with Ω_c/Ω_v/Ω_b = 0.6/0.3/0.1 is compatible with the damped Lyα data only at ≤ 2.5, but that it is probably incompatible with the z > 3 damped Lyα data. The situation is uncertain because there is very little data for z > 3. The predictions of CHDM are quite sensitive to the hot (neutrino) fraction, and we find that Ω_c/Ω_v/Ω_b = 0.725/0.20/0.075 (and possibly even Ω_c/Ω_v/Ω_b = 0.675/0.25/0.075) is compatible with the z > 3 data. With one massive neutrino species, using Ω_v = 0.20 instead of 0.30 corresponds to lowering the neutrino mass from 7.0 to 4.7 eV, for H_0 = 50 km s~(-1) Mpc~(-1) and T = 2.726 K. In CHDM, the higher redshift damped Lyα systems are predicted to have lower masses (～ 3 x 10~(10) solar mass at z = 3), a prediction which can be checked by measuring the velocity widths of the associated metal-line systems. Predictions for high-z objects crucially depend on the effects of limited resolution and the finite box size in N-body simulations or on the parameters of the Press-Schechter approximation, if it is used. By analyzing our numerical simulations with vastly different resolutions and box sizes as well as those of Ma & Bertschinger (1994), we show that for the CHDM models with Ω_v = 0.2-0.3 the Press-Schechter approximation should be used with Gaussian filter with δ_c = 1.5 if halos are defined with the mean overdensity larger than 200. If one tries to recover the total mass of a collapsed halo, a better value for the collapse parameter is δ_c = 1.40. We argue that nonlinear effects due to waves both longer and shorter than those considered in numerical simulations could probably result in δ_c as low as δ_c = 1.3.
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