Let X be an irreducible rational nodal curve of arithmetic genus g > 2, and let S* be a non-special, effective invertible sheaf on X . Let W( = S ? ) denote the set of smooth Weierstrass points of 3? and all its positive tensor powers on I. In this paper, we study the distribution of W{3?) on X. In particular, we will show that is not dense on X, generalizing an example of R. F. Lax.
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