Geodesic
Projective Geometry Related to the Singularities of Theta Divisors of Jacobians
Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 93-109.

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By studying the higher order focal properties of a family of linear spaces naturally associated to the singular locus of the theta divisor of a non-hyperelliptic jacobian of genus $g \ge 5$, we give a new proof of the classical theorem of Torelli. Related questions and open problems are also discussed. 
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Ciliberto, C.; Sernesi, E. Projective Geometry Related to the Singularities of Theta Divisors of Jacobians. Bollettino della Unione matematica italiana, Série 9, Tome 3 (2010) no. 1, pp. 93-109. http://geodesic.mathdoc.fr/item/BUMI_2010_9_3_1_a2/

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