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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     author = {A. N. Tyurin},
     title = {On the set of singularities of the {Poincar\'e} divisor of the {Picard} variety of the {Fano} surface of a~nonsingular cubic},
     journal = {Izvestiya. Mathematics },
     pages = {938--948},
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     volume = {6},
     number = {5},
     year = {1972},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a2/}
}
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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/