Summary
In this paper we consider the family of curves of genus g=2m with a g 13 lying on a particular rational normal scroll S in Pg− 1(C). We define a covering of this family representing the Weierstrass points and we study the monodromy. Applying the techniques of [3] we prove that if g=4 the monodromy is the full symmetric group and for general g=2m it is transitive. We show also that the generic curve of the family has only normal Weierstrass points generalizing a classical result. We work always over the complex numbers.
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Partially supported by: Ministero della Pubblica Istruzione - Italia; Consiglio Nazionale delle Ricerche — Italia.
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Canuto, G. On the monodromy of weierstrass points. Annali di Matematica pura ed applicata 136, 49–63 (1984). https://doi.org/10.1007/BF01773376
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DOI: https://doi.org/10.1007/BF01773376