We report upper limits on the masses of black holes that can be present in the centers of 16 nearby galaxy bulges. These limits for our statistically complete sample were derived from the modeling of the central emission-line widths ([N II] or [S II]), observed over a 0.25 X 0.2 (R < 9 pc) aperture. The experiment has a mean detection sensitivity of 3.9 X 10^6 solar masses. For three sample members with direct determinations of black hole masses our upper limits agree within the uncertainties, while in general our upper limits are found to be close to the masses measured in other bulges with global properties similar to ours. Remarkably, our limits lie quite closely to the recently derived relation between black hole mass and stellar velocity dispersion. These results support a picture wherein the black hole mass and overall galaxy structure are closely linked, as galaxies with exceptionally high black hole masses at a given velocity dispersion apparently are rare.
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