Beauville, Arnaud Variétés de Prym et jacobiennes intermediaires. (French) Zbl 0368.14018 Ann. Sci. Éc. Norm. Supér. (4) 10, 309-391 (1977). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 14 ReviewsCited in 165 Documents MSC: 14M20 Rational and unirational varieties 14K30 Picard schemes, higher Jacobians × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] S. S. ABHYANKAR , Resolution of Singularities of Embedded Algebraic Surfaces , Academic Press 1966 . MR 36 #164 | Zbl 0147.20504 · Zbl 0147.20504 [2] A. ANDREOTTI and A. MAYER , On Period Relations for Abelian Integrals on Algebraic Curves (Ann. Scuola Norm. Sup., Pisa, vol. 21, 1971 ). Numdam | MR 36 #3792 | Zbl 0222.14024 · Zbl 0222.14024 [3] M. ARTIN and D. MUMFORD , Some Elementary Examples of Unirational Varieties which are not Rational (Proc. London Math. Soc. (3), vol. 25, 1972 , p. 75-95). MR 48 #299 | Zbl 0244.14017 · Zbl 0244.14017 · doi:10.1112/plms/s3-25.1.75 [4] A. BEAUVILLE , Prym Varieties and Schottky Problem (Inventiones Math., vol. 41, Fasc 2, 1977 ). MR 58 #27995 | Zbl 0333.14013 · Zbl 0333.14013 · doi:10.1007/BF01418373 [5] C. H. CLEMENS and P. A. GRIFFITHS , The Intermediate Jacobian of the Cubic Threefold (Ann. of Math., vol. 95, 1972 , p. 281-356). MR 46 #1796 | Zbl 0214.48302 · Zbl 0214.48302 · doi:10.2307/1970801 [6] P. DELIGNE , Théorie de Hodge II (Publ. Math., I.H.E.S., n^\circ 40). Numdam | Zbl 0219.14007 · Zbl 0219.14007 · doi:10.1007/BF02684692 [7] A. C. DIXON , Note on the Reduction of a Ternary Quantic to a Symmetrical Determinant (Proc. Cambridge Phil. Soc., vol. 11, 1902 , p. 350-351). JFM 33.0172.05 [8] A. GROTHENDIECK , Éléments de Géométrie Algébrique (Publ. Math. I.H.E.S.). Numdam · Zbl 0203.23301 [9] G. FANO , Su alcune varietà algebriche a tre dimensioni aventi curve sezioni canoniche , Scritti matematici offerti a Luigi Berzolari, Pavia 1936 . JFM 62.0780.01 · JFM 62.0780.01 [10] G. FANO , Sulle sezioni spaziali della varietà grassmanniana delle rette dello spazio a cinque dimensioni (Rend. Accad. Lincei (6), vol. 11, 1er sem. 1930 , p. 329). JFM 56.0575.03 · JFM 56.0575.03 [11] P. A. GRIFFITHS , Periods of Integrals on Algebraic Manifolds (Bull. Amer. Math. Soc., vol. 76, 1970 , p. 228-296). Article | MR 41 #3470 | Zbl 0214.19802 · Zbl 0214.19802 · doi:10.1090/S0002-9904-1970-12444-2 [12] P. A. GRIFFITHS , Some Transcendental Methods in the Study of Algebraic Cycles (Proc. of the Maryland Conference on Complex Analysis, Lecture Notes in Math., vol. 185, Springer-Verlag). MR 46 #9041 | Zbl 0208.48502 · Zbl 0208.48502 [13] P. A. GRIFFITHS , On the Periods of Certain Rational Integrals : I and II (Ann. of Math., vol. 90, n^\circ 3, 1969 , p. 460-541). MR 41 #5357 | Zbl 0215.08103 · Zbl 0215.08103 · doi:10.2307/1970746 [14] F. HIRZEBRUCH , Topological Methods in Algebraic Geometry (3e édition), Springer-Verlag. Zbl 0376.14001 · Zbl 0376.14001 [15] W. HOYT , On Products and Algebraic Families of Jacobian Varieties (Ann. of Math., vol. 77, 1963 , p. 415-423). MR 27 #148 | Zbl 0154.20701 · Zbl 0154.20701 · doi:10.2307/1970125 [16] HODGE and PEDOE , Methods of Algebraic Geometry , Cambridge University Press, 1947 . MR 10,396b · Zbl 0055.38705 [17] V. A. ISKOVSKI and Y. MANIN , Three-Dimensional Quartics and Counterexamples to the Lüroth Problem (Mat. Sbornik, vol. 86, n^\circ 1, 1971 ). Zbl 0222.14009 · Zbl 0222.14009 [18] S. LANG , On Quasi-Algebraic Closure (Ann. of Math., vol. 55, 1952 , p. 373-390). MR 13,726d | Zbl 0046.26202 · Zbl 0046.26202 · doi:10.2307/1969785 [19] S. LANG , Abelian Varieties , Interscience Wiley, New York, 1959 . MR 21 #4959 | Zbl 0098.13201 · Zbl 0098.13201 [20] LASCU , MUMFORD and SCOTT , The Self-Intersection Formula and the “Formule-Clef” (Proc. of the Cambridge Philosophical Society, vol. 78, 1975 , p. 117-123). MR 56 #354 | Zbl 0341.14002 · Zbl 0341.14002 · doi:10.1017/S0305004100051550 [21] D. MUMFORD , Prym Varieties I (Contributions to Analysis, Academic Press, New York, 1974 ). MR 52 #415 | Zbl 0299.14018 · Zbl 0299.14018 [22] D. MUMFORD , Further Comments on Boundary Points (Woods Hole Summer Institute in Algebraic Geometry, 1964 ). [23] D. MUMFORD , Theta Characteristics of an Algebraic Curve (Ann. Sc. Éc. Norm. Sup., vol. 4, 1971 ). Numdam | MR 45 #1918 | Zbl 0216.05904 · Zbl 0216.05904 [24] D. MUMFORD , Varieties Defined by Quadratic Equations (C.I.M.E., Varenna, 1969 ). Zbl 0198.25801 · Zbl 0198.25801 [25] D. MUMFORD , Abelian varieties , Oxford University Press, ( 1970 ). MR 44 #219 | Zbl 0223.14022 · Zbl 0223.14022 [26] J. P. MURRE , Algebraic Equivalence Modulo Rational Equivalence on a Cubic Threefold (Compositio Math., vol. 25, 1972 ). Numdam | MR 50 #4576a | Zbl 0242.14002 · Zbl 0242.14002 [27] J. P. MURRE , Reduction of the Proof of the Non-Rationality of a Non-Singular Cubic Threefold to a Result of Mumford (Compositio Math., vol. 27, 1973 ). Numdam | MR 50 #4576b | Zbl 0271.14020 · Zbl 0271.14020 [28] J. P. MURRE , Some Results on Cubic Threefolds , dans Classification of Algebraic Varieties and Compact Complex Manifolds (Lecture Notes, n^\circ 412, Springer-Verlag). MR 51 #10345 | Zbl 0299.14019 · Zbl 0299.14019 [29] L. ROTH , Sulle V3 algebriche su cui l’aggiunzione si estingue (Rend. Acc. Lincei (8), vol. 9, 1950 , p. 246). MR 12,739f | Zbl 0040.08301 · Zbl 0040.08301 [30] S. RECILLAS , Jacobians of Curves with g1’4 s are the Prym’s of Trigonal Curves (Bol. de la Soc. Mat. Mexicana, vol. 19, n^\circ 1, 1974 ). MR 58 #666 | Zbl 0343.14012 · Zbl 0343.14012 [31] P. SAMUEL , Relations d’équivalence en géométrie algébrique (Proc. Inter. Congress Math., Edimbourg, 1958 , p. 470-487). MR 22 #6807 | Zbl 0119.36901 · Zbl 0119.36901 [32] Séminaire Cartan 1957 - 1958 (10e année) : Fonctions automorphes . Numdam | Zbl 0101.05601 · Zbl 0101.05601 [33] Séminaire Chevalley 1958 (2e année) : Anneaux de Chow et applications . Numdam [34] A. GROTHENDIECK et coll., Séminaire de Géométrie algébrique (Lecture Notes, Springer-Verlag). · Zbl 0122.16102 [35] J. G. SEMPLE et L. ROTH , Introduction to Algebraic Geometry , Oxford, Clarendon, 1949 . MR 11,535d | Zbl 0041.27903 · Zbl 0041.27903 [36] A. N. TJURIN , On the Intersections of Quadrics (Russian Math. Surveys, vol. 30, n^\circ 6, 1975 ). MR 54 #12791 | Zbl 0339.14020 · Zbl 0339.14020 · doi:10.1070/RM1975v030n06ABEH001530 [37] A. N. TJURIN , The Geometry of the Poincaré Theta-Divisor of a Prym Variety [Izvestia Mat., 39, n^\circ 5, 1975 (en russe)]. MR 54 #2664 | Zbl 0339.14017 · Zbl 0339.14017 · doi:10.1070/IM1975v009n05ABEH001513 [38] S. ZUCKER , Generalized Intermediate Jacobians and the Theorem on Normal Functions (Inventiones Math., vol. 33, 1976 , p. 185-222). MR 54 #313 | Zbl 0329.14008 · Zbl 0329.14008 · doi:10.1007/BF01404203 This reference list is based on information provided by the publisher or from digital mathematics libraries. 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