Recovering plane curves from their bitangents

Abstract

We prove that a general complex projective plane quartic curve is uniquely determined by its 28 bitangent lines. A similar property (called theta-property in the paper) is proved for a general singular quartic having δ = 1 , … , 4 \delta =1,\dots ,4 double points with respect to its set of generalized bitangents (suitably defined). The proofs are by degeneration.