Recovering plane curves of low degree from their inflection lines and   inflection points
  In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree at least three from its inflection lines? We answer positively to the posed question for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve. 
Marco Pacini, Damiano Testa
math.AG