Geodesic
Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 230-253.

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We classify some special classes of nonrational Fano threefolds with terminal singularities. In particular, all such hyperelliptic and trigonal varieties are found. 
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Yuri G. Prokhorov. Rationality of Fano Threefolds with Terminal Gorenstein Singularities. I. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra, number theory, and algebraic geometry, Tome 307 (2019), pp. 230-253. http://geodesic.mathdoc.fr/item/TM_2019_307_a12/

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