# 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 $dim\phantom{\rule{0.277778em}{0ex}}\left({W}_{4}^{1}\right)=1$

Open Mathematics (2016)

- Volume: 14, Issue: 1, page 1-12
- ISSN: 2391-5455

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topMarc 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 -

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