3
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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 $Pic^0(T)$?

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  • $\begingroup$ By a theorem of Welters, $h^{1,0}=0$, so it should be zero.. $\endgroup$ – Walter Neff Feb 19 '15 at 20:04
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    $\begingroup$ 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). $\endgroup$ – abx Feb 19 '15 at 20:53

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