On a Family of Special Linear Systems on Algebraic Curves

1984 ◽  
Vol 90 (3) ◽  
pp. 355
Author(s):  
Edmond E. Griffin II
2015 ◽  
Vol 15 (2) ◽  
Author(s):  
Jean-Philippe Monnier

AbstractGiven a real curve, we study special linear systems called “very special” for which the dimension does not satisfy a Clifford type inequality.We classify all these very special linear systems when the gonality of the curve is small.


2002 ◽  
Vol 13 (01) ◽  
pp. 11-29 ◽  
Author(s):  
KYUNG-HYE CHO ◽  
CHANGHO KEEM ◽  
AKIRA OHBUCHI

We classify smooth projective algebraic curves C of genus g such that the variety of special linear systems [Formula: see text] has dimension g- 7. We first prove that if [Formula: see text] has dimension g-7≥0 then C is either trigonal, tetragonal, a double covering of a curve of genus 2 or a smooth plane sextic. This result establishes the next extension of dimension theorems of H. Martens and D. Mumford on the variety of special linear systems with the fullest possible generality. We then proceed to show that, under the assumption g≥11, [Formula: see text] has dimension g- 7 if and only if C is either a trigonal curve or a double covering of a curve of genus 2.


2008 ◽  
Vol 59 (3) ◽  
pp. 239-254 ◽  
Author(s):  
Alberto Alzati

2016 ◽  
Vol 14 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marc Coppens

AbstractFor all integers g ≥ 6 we prove the existence of a metric graph G with $w_4^1 = 1$ such that G has Clifford index 2 and there is no tropical modification G′ of G such that there exists a finite harmonic morphism of degree 2 from G′ to a metric graph of genus 1. Those examples show that not all dimension theorems on the space classifying special linear systems for curves have immediate translation to the theory of divisors on metric graphs.


2010 ◽  
Vol 27 (2) ◽  
pp. 212-231 ◽  
Author(s):  
Sonia Pérez-Díaz ◽  
J. Rafael Sendra ◽  
Sonia L. Rueda ◽  
Juana Sendra

2019 ◽  
Vol 223 (8) ◽  
pp. 3225-3237
Author(s):  
Joaquín Moraga

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