Geodesic
The geometry of the Fano surface of the double cover of $P^3$ branched in a~quartic
Izvestiya. Mathematics , Tome 16 (1981) no. 2, pp. 373-397

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This paper gives a computation of the irregularity of the Fano surface $\mathscr F$ of lines on the double cover $X\to P^3$ branched in a quartic. A tangent bundle theorem is proved for $\mathscr F$, from which it follows that $\mathscr F$ determines $X$ uniquely. It is shown that the Abel–Jacobi map $a\colon\operatorname{Alb}(\mathscr F)\to J_3(X)$ is an isogeny. Bibliography: 7 titles. 
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     title = {The geometry of the {Fano} surface of the double cover of $P^3$ branched in a~quartic},
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A. S. Tikhomirov. The geometry of the Fano surface of the double cover of $P^3$ branched in a~quartic. Izvestiya. Mathematics , Tome 16 (1981) no. 2, pp. 373-397. http://geodesic.mathdoc.fr/item/IM2_1981_16_2_a6/