# Pic^0 of the surface of bitangents of a quartic

Let $S$ be a generic quartic surface in $\mathbf{P}^3$. Let $T$ be the surface of the lines bitangent to $S$.

What can we say about $Pic^0(T)$?

• By a theorem of Welters, $h^{1,0}=0$, so it should be zero.. – Walter Neff Feb 19 '15 at 20:04
• It is indeed zero. This is Corollary 3.44 in Welters' thesis: Abel-Jacobi Isogenies for Certain Types of Fano Threefolds, Math. Centrum, Amsterdam (1981). – abx Feb 19 '15 at 20:53