Lifting tropical bitangents
| Autor: | Yoav Len, Hannah Markwig |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics |
| Rok vydání: | 2020 |
| Předmět: |
T-NDAS
010103 numerical & computational mathematics 01 natural sciences Combinatorics Lift (mathematics) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Tropical geometry Quartic function FOS: Mathematics Mathematics - Combinatorics QA Mathematics 0101 mathematics Algebraic number QA Algebraic Geometry (math.AG) Physics::Atmospheric and Oceanic Physics Bitangent Mathematics Algebra and Number Theory 010102 general mathematics Computational Mathematics Bitangents of quartics Combinatorics (math.CO) Algebraic curve |
| Zdroj: | Journal of Symbolic Computation. 96:122-152 |
| ISSN: | 0747-7171 |
| DOI: | 10.1016/j.jsc.2019.02.015 |
| Popis: | 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. 35 pages, 24 figures, 1 table. Minor changes. Accepted for publication in Journal of Symbolic Computation |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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