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Lifting tropical bitangents. (English) Zbl 07074721
Summary: 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.

##### MSC:
 14T05 Tropical geometry (MSC2010) 68W30 Symbolic computation and algebraic computation
##### Keywords:
tropical geometry; bitangents of quartics
##### Software:
SINGULAR; Book3264Examples; tropical.lib; Viro.sage
Full Text:
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