We review observations in lambda-5007 which reveal an ellipse of line emission around SN 1987A. Spectroscopy suggests that it is an inclined ring of gas, presumably excited by the UV flash associated with shock breakout. The occurrence of this flash was confirmed earlier by IUE observations of narrow fluorescent lines from the SN. We derive a simple expression for the rate at which the kinematically accessible paraboloid sweeps over the length of a thin uniform circular ring, and present a simple integral expression for the light curve F(t) of a fluorescent line in terms of epsilon(t), the local line emissivity. Our resulting light curves agree well with computations by Lundqvist but not so well with those by Panagia and Gilmozzi. This, together with the variety of possible light curves and the uncertainties in the ring geometry and morphology, suggests that the claimed error bar (+/- 6%) on the distance determination by Panagia et al. should be treated with caution. We graph many simple examples of the relationship between epsilon(t) and F(t) and use the results to deduce the characteristics of the local emissivity functions which will produce the best fit to the observed N III] lambda-1750 and N V lambda-1240 light curves. Adopting physical models by Lundqvist and Fransson for an optically thin gas, in which the functions epsilon(t) for these lines peak only after recombination has occurred, we find poor agreement with the observed light curves for these lines. Better agreement is obtained if epsilon(t) responds quickly to the UV flash and persists approximately 300 days afterwards (suggesting that the ring may have been optically thick to the UV flash); a characteristic arcsine shape is then seen on the leading side of the light curve. The different shape of the N IV] lambda-1485 light curve remains a puzzle. We invert the N III and N V light curves to find the functions epsilon(t) which give best fits to the observations. The inversions are affected by scatter in the data. Nevertheless they give marginal evidence that an additional gas cloud is contributing to the UV line fluxes at t greater than or similar to 700 days.