# Local structure of the surface of bitangents to a quartic

Let $S \subset \mathbb{P}^3$ be a (possibly singular) quartic. I need some information about the local structure of the surface $Bit(S)$ of bitangents to $S$. I have done the computations, but they are a bit heavy, and I'd be happier if I could just cite a reference. In particular I need a local description of $Bit(S)$ around a line joining two isolated nodes.

The book Abel-Jacobi isogenies for certain types of Fano threefolds by Welters studies the surface of bitangents in some detail, but it soon restricts to the case of smooth $S$.

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