A metric graph satisfying [...] w 4 1 = 1 $w_4^1=1$ that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 $dim\left(W_4^1\right)=1$

Marc Coppens. "A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$." Open Mathematics 14.1 (2016): 1-12. <http://eudml.org/doc/276926>.

@article{MarcCoppens2016,
abstract = {For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1$w_4^1 = 1$ 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.},
author = {Marc Coppens},
journal = {Open Mathematics},
keywords = {Metric graphs; Curves; Lifting problems; Special divisors; Clifford index; Dimension theorems; metric graphs; curves; lifting problems; special divisors; dimension theorems},
language = {eng},
number = {1},
pages = {1-12},
title = {A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$},
url = {http://eudml.org/doc/276926},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Marc Coppens
TI - A metric graph satisfying [...] w 4 1 = 1 $w_4^1 = 1$ that cannot be lifted to a curve satisfying [...] dim ⁡   ( W 4 1 ) = 1 $\dim \;(W_4^1 ) = 1$
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 1
EP - 12
AB - For all integers g ≥ 6 we prove the existence of a metric graph G with [...] w41=1$w_4^1 = 1$ 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.
LA - eng
KW - Metric graphs; Curves; Lifting problems; Special divisors; Clifford index; Dimension theorems; metric graphs; curves; lifting problems; special divisors; dimension theorems
UR - http://eudml.org/doc/276926
ER -