We report high-resolution florescence studies of the rotational structure of the Hg,4r A (3)0(+) -X (1)0(+) (1 less than or equal to v’less than or equal to(,) v "=0) vibrational bands which occur near to the Hg 6s(2) S-1(0)-6s6p P-3(1) (254 nm) atomic resonance. The molecules were formed in a supersonic jet expansion and were excited by UV radiation produced by intracavity second-harmonic generation in a cw dye laser. The intensity profile of each band was reproduced by a theoretical model. Least-squares fits to the experimental spectra yielded accurate values for the band origins, rotational constants, and isotope shifts. This information was used in a Rydberg-Klein-Rees evaluation of the A (3)0(+) potential, which was found to differ slightly, but significantly, from a Morse function in the region probed by this experiment.