BOUNDS FOR THE GENUS OF SPACE-CURVES

We compute the following upper bounds for the maximal arithmetic genus P-a(d,t) over all locally Cohen-Macaulay space curves of degree d, wh ich are not contained in a surface of degree t - 1: P-a(d,t) less than or equal to {t - 1)d + 1- (t + 2/3) if t less than or equal to d less than or equal to 2t, 1/2(d - t)(d - t - 1) - (t - 1/3) if d greater t han or equal to 2t + 1. These bounds are sharp for t less than or equa l to 4 and any d greater than or equal to t.