We present new IRAM PdBI 1.3mm continuum observations at ~1.5 resolution of 28 SMGs previously discovered with the 870um bolometer LABOCA at APEX within the central 0.7deg2 of the COSMOS field. 19 out of the 28 LABOCA sources were detected with the PdBI at a >~3sigma level of ~1.4mJy/b. A combined analysis of this new sample with existing interferometrically identified SMGs in the COSMOS field yields the following results: 1) >~15%, and possibly up to ~40% of single-dish detected SMGs consist of multiple sources, 2) statistical identifications of multi-wavelength counterparts to the single-dish SMGs yield that only ~50% of these single-dish SMGs have real radio or IR counterparts, 3) ~18% of interferometric SMGs have only radio or even no multi-wavelength counterpart at all, and 4) ~50-70% of z>~3 SMGs have no radio counterparts down to an rms of 7-12uJy at 1.4GHz. Using the exact interferometric positions to identify proper multi-wavelength counterparts allows us to determine accurate photometric redshifts for these sources. The redshift distributions of the combined and the individual 1.1mm and 870um selected samples have a higher mean and broader width than the redshift distributions derived in previous studies. Our sample supports the previous tentative trend that on average brighter and/or mm-selected SMGs are located at higher redshifts. There is a tentative offset between the mean redshift for the 1.1mm (<z>=3.1+/-0.4) and 870um (<z>=2.6+/-0.4) selected samples, with the 1.1mm sources lying on average at higher redshifts. Based on our nearly complete sample of AzTEC 1.1mm SMGs within a uniform 0.15deg2 area we infer a higher surface density of z>~4 SMGs than predicted by current cosmological models. In summary, our findings imply that (sub-)millimeter interferometric identifications are crucial to build statistically complete and unbiased samples of SMGs.
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