On the distribution of Weierstrass points on Gorenstein quintic curves

Abstract

Abstract This paper is concerned with developing a technique to compute in a very precise way the distribution of Weierstrass points on the members of any 1-parameter family Ca, a ∈ C , of Gorenstein quintic curves with respect to the dualizing sheaf K C a . The nicest feature of the procedure is that it gives a way to produce examples of existence of Weierstrass points with prescribed special gap sequences, by looking at plane curves or, more generally, to subcanonical curves embedded in some higher dimensional projective space.