Lifting tropical bitangents
Date
01/2020Metadata
Show full item recordAbstract
We study lifts of tropical bitangents to the tropicalization of a given complex algebraic curve together with their lifting multiplicities. Using this characterization, we show that generically all the seven bitangents of a smooth tropical plane quartic lift in sets of four to algebraic bitangents. We do this constructively, i.e. we give solutions for the initial terms of the coefficients of the bitangent lines. This is a step towards a tropical proof that a general smooth quartic admits 28 bitangent lines. The methods are also appropriate to count real bitangents, however the conditions to determine whether a tropical bitangent has real lifts are not purely combinatorial.
Citation
Len , Y & Markwig , H 2020 , ' Lifting tropical bitangents ' , Journal of Symbolic Computation , vol. 96 , pp. 122-152 . https://doi.org/10.1016/j.jsc.2019.02.015
Publication
Journal of Symbolic Computation
Status
Peer reviewed
ISSN
0747-7171Type
Journal article
Rights
Copyright © 2019 Elsevier Ltd. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1016/j.jsc.2019.02.015
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