The non rationality of the generic Enriques' threefold

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1. [1] A. Beauville: Variétés de Prym et Jacobiennes intermédiaires, Ann. Scient. de l'Ecole Norm. Sup.10 (1977), 304-392. Zbl0368.14018MR472843
2. [2] A. Beauville: Prym varieties and Schottky problem, Invent. Math.41, fasc. 2, (1977) 149-196. Zbl0333.14013MR572974
3. [3] C. Clemens and PH. Griffiths: On the intermediate Jacobian of the cubic threefold, Ann. Math.95 no. 2 (1972) 281-356. Zbl0214.48302MR302652
4. [4] A. Conte and J.P. Murre: On quartic threefolds with a double line, Indag. Math. 80 (1977) 145-175. Zbl0353.14016MR498594
5. [5] PH. Griffiths and J. Harris: Principles of Algebraic Geometry, Wiley Interscience Pub., New York, 1974. 
6. [6] D. Mumford: "Prym Varieties I" in Contribution to Analysis, Academic Press, New York (1974) 325-350. Zbl0299.14018MR379510
7. [7] D. Mumford: Curves and their Jacobians. Univer. of Michigan Press9175. Zbl0316.14010MR419430
8. [8] J.P. Murre: Reduction of the proof of the non rationality of the non singular cubic threefold to a result of Mumford, Compos. Math.27 no. 1 (1972) 63-82. Zbl0271.14020MR352089
9. [9] J.P. Murre: Algebraic equivalence modulo rational equivalence on a cubic threefold, Comp. math. 25 (1972) 161-206. Zbl0242.14002MR352088
10. [10] L. Roth: Algebraic threefolds. Springer Verl., Berlin1955. Zbl0066.14704MR48083
11. [11] L. Roth: Lezioni di Geometria Algebrica Classica, Pubblicazioni dell'Istituto di Matematica dell'Università diGenova, no. 10 (1955). Zbl0068.14503
12. [12] J.P. Serre: On the foundamental group of a unirational variety, J. Lond. Math. Soc.34 (1959) 481-484. Zbl0097.36301MR109155
13. [13] Tyrrel: The Enriques threefold, Proc. Cambridge Philos. Soc. no.57 (1961) 897-898. Zbl0163.15401MR130254

1. A. Conte, J. P. Murre, Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces
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