On the variety of special linear systems on an algebraic curve

1990 ◽  
Vol 288 (1) ◽  
pp. 309-322 ◽  
Author(s):  
C. Keem
Keyword(s):  
Linear Systems ◽  
Algebraic Curve ◽  
Special Linear

scholarly journals Special linear systems and syzygies

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

scholarly journals A metric graph satisfying w41=1$w_4^1 = 1$ that cannot be lifted to a curve satisfying dim⁡ (W41)=1$\dim \;(W_4^1 ) = 1$

2016 ◽  
Vol 14 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Marc Coppens
Keyword(s):  
Linear Systems ◽  
Harmonic Morphism ◽  
Metric Graphs ◽  
Clifford Index ◽  
Special Linear ◽  
Metric Graph ◽  
Index 2

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.

scholarly journals On a notion of toric special linear systems

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

scholarly journals Green’s conjecture for curves on arbitrary K3 surfaces

2011 ◽  
Vol 147 (3) ◽  
pp. 839-851 ◽  
Author(s):  
Marian Aprodu ◽  
Gavril Farkas
Keyword(s):  
Algebraic Curve ◽  
Complete Solution ◽  
K3 Surfaces ◽  
Linear Series ◽  
Canonical Embedding ◽  
Smooth Curves ◽  
Special Linear

AbstractGreen’s conjecture predicts than one can read off special linear series on an algebraic curve, by looking at the syzygies of its canonical embedding. We extend Voisin’s results on syzygies of K3 sections, to the case of K3 surfaces with arbitrary Picard lattice. This, coupled with results of Voisin and Hirschowitz–Ramanan, provides a complete solution to Green’s conjecture for smooth curves on arbitrary K3 surfaces.

scholarly journals The Gonality Sequence of Complete Graphs

10.37236/6876 ◽  
2017 ◽  
Vol 24 (4) ◽  
Author(s):  
Filip Cools ◽  
Marta Panizzut
Keyword(s):  
Linear Systems ◽  
Complete Graph ◽  
Algebraic Curve ◽  
Plane Curve ◽  
Finite Graph ◽  
Complete Graphs ◽  
Metric Graphs ◽  
Smooth Plane ◽  
Graph Metric ◽  
Gonality Sequence

The gonality sequence $(\gamma_r)_{r\geq1}$ of a finite graph/metric graph/algebraic curve comprises the minimal degrees $\gamma_r$ of linear systems of rank $r$. For the complete graph $K_d$, we show that $\gamma_r =  kd - h$ if $r<g=\frac{(d-1)(d-2)}{2}$, where $k$ and $h$ are the uniquely determined integers such that $r = \frac{k(k+3)}{2} - h$ with $1\leq k\leq d-3$ and $0 \leq h \leq k $. This shows that the graph $K_d$ has the gonality sequence of a smooth plane curve of degree $d$. The same result holds for the corresponding metric graphs.

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