Lifting tropical bitangents

Yoav Len, Hannah Markwig

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.
Original languageEnglish
Pages (from-to)122-152
JournalJournal of Symbolic Computation
Volume96
Early online date1 Mar 2019
DOIs
Publication statusPublished - Jan 2020

Keywords

  • Tropical geometry
  • Bitangents of quartics

Fingerprint

Dive into the research topics of 'Lifting tropical bitangents'. Together they form a unique fingerprint.

Cite this