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On certain loci of curves of genus g [ges ] 4 with Weierstrass points whose first non-gap is three

Published online by Cambridge University Press:  17 June 2002

G. CASNATI  and
A. DEL CENTINA
G. CASNATI
Affiliation:
Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10139 Torino, Italy. e-mail: casnati@calvino.polito.it
A. DEL CENTINA
Affiliation:
Dipartimento di Matematica, Università degli Studi di Ferrara, via Machiavelli 35, 44100 Ferrara, Italy. e-mail: cen@dns.unife.it
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Abstract

Let [Mfr ]g be the moduli space of smooth curves of genus g [ges ] 4 over the complex field [Copf ] and let [Tfr ]g ⊆ [Mfr ]g be the trigonal locus, i.e. the set of points [C] ∈ [Mfr ]g representing trigonal curves C of genus g [ges ] 4. Recall that each such curve C carries exactly one g13 (respectively at most two) if g [ges ] 5 (respectively g = 4). Let |D| be a g13 on C and suppose that it has a total ramification point at P (t.r. for short), i.e. that there is on C a point P such that 3P ∈ |D|. Such a P is a Weierstrass point whose first non-gap is three. In the present paper we study some sub-loci of [Tfr ]g related to curves possessing such points.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 132 , Issue 3 , May 2002 , pp. 395 - 407
Copyright
2002 Cambridge Philosophical Society

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