Weierstrass points on trigonal curves I: The ramification points

1988 ◽  
Vol 37 (3) ◽  
pp. 321-350
Author(s):  
Marc Coppens
Keyword(s):  
Weierstrass Points ◽  
Trigonal Curves ◽  
Ramification Points

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

2002 ◽  
Vol 132 (3) ◽  
pp. 395-407 ◽  
Author(s):  
G. CASNATI ◽  
A. DEL CENTINA
Keyword(s):  
Moduli Space ◽  
Weierstrass Point ◽  
Complex Field ◽  
Ramification Point ◽  
Smooth Curves ◽  
Weierstrass Points ◽  
Trigonal Curves ◽  
Set Of Points

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.

scholarly journals On the distribution of ramification points in trigonal curves

1999 ◽  
Vol 22 (3) ◽  
pp. 489-496
Author(s):  
Cícero F. Carvalho
Keyword(s):  
Rational Curves ◽  
Trigonal Curve ◽  
Trigonal Curves ◽  
Rational Normal Scroll ◽  
Ramification Points

We study the distribution of the total and ordinary ramification points of a trigonal curve over the intersection of this curve with rational curves on a rational normal scroll. We show, among other results, that these intersections may contain all the ramification points of the trigonal curve.

On the varieties parametrinzing trigonal curves with assigned weierstrass points

1998 ◽  
Vol 26 (10) ◽  
pp. 3291-3312 ◽  
Author(s):  
Michela Brundu ◽  
Gianni Sacchiero
Keyword(s):  
Weierstrass Points ◽  
Trigonal Curves

On Higher Order Weierstrass Points

1972 ◽  
Vol 95 (2) ◽  
pp. 357 ◽  
Author(s):  
Bruce A. Olsen
Keyword(s):  
Higher Order ◽  
Weierstrass Points
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