Geodesic
On the set of singularities of the Poincar\'e divisor of the Picard variety of the Fano surface of a~nonsingular cubic
Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 938-948.

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In the paper it is proved that the singular points of the Poincaré divisor of the Picard variety of the Fano surface of a nonsingular cubic are contained in the set of points of second and third orders of the abelian variety or in elliptic curves corresponding to the inflection points of the cubic. 
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A. N. Tyurin. On the set of singularities of the Poincar\'e divisor of the Picard variety of the Fano surface of a~nonsingular cubic. Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 938-948. http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a2/

[1] Bombieri E., Swinnerton-Dyer H. P. F., “On the local Zeta-function of a cubic threefold”, Annali della Scuola Normale superiore di Pisa (III), XXI:1 (1967), 1–29 | MR

[2] Tyurin A. N., “Geometriya poverkhnosti Fano neosoboi kubiki $F\subset P^4$ i teoremy Torelli dlya poverkhnostei Fano i kubik”, Izv. AN SSSR. Ser. matem., 35 (1971), 498–529 | Zbl