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Gonality of complete graphs with a small number of omitted edges
Author(s) -
Panizzut Marta
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500354
Subject(s) - mathematics , combinatorics , lift (data mining) , gravitational singularity , graph , morphism , mathematical analysis , computer science , data mining
Let K d be the complete metric graph on d vertices. We compute the gonality of graphs obtained from K d by omitting edges forming a K h , or general configurations of at most d − 2 edges. We also investigate if these graphs can be lifted to curves with the same gonality. We lift the former graphs and the ones obtained by removing up to d − 2 edges not forming a K 3 using models of plane curves with certain singularities. We also study the gonality when removing d − 1 edges not forming a K 3 . We use harmonic morphism to lift these graphs to curves with the same gonality because in this case plane singular models can no longer be used due to a result of Coppens and Kato.