On the distribution of Weierstrass points on irreducible rational nodal curves

John B. Little and Kathryn A. Furio

Vol. 144 (1990), No. 1, 131–136

DOI: 10.2140/pjm.1990.144.131

Abstract

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

Mathematical Subject Classification 2000

Primary: 14H55

Secondary: 14H20, 14H45

Milestones

Received: 9 September 1988

Published: 1 July 1990