Little, John Translation manifolds and the converse of Abel’s theorem. (English) Zbl 0521.14017 Compos. Math. 49, 147-171 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 2 Documents MSC: 14K20 Analytic theory of abelian varieties; abelian integrals and differentials 14H40 Jacobians, Prym varieties 14J25 Special surfaces Keywords:converse of Abel theorem; translation manifold; Lie-Wirtinger theorem; non-degenerate doubly translation type hypersurface; n-dimensional principally polarized abelian variety; canonically polarized Jacobian of smooth nonhyperelliptic curve PDF BibTeX XML Cite \textit{J. Little}, Compos. Math. 49, 147--171 (1983; Zbl 0521.14017) Full Text: Numdam EuDML References: [1] A. Altman , and S. Kleiman : Introduction to Grotendieck Duality Theory . Lecture Notes in Mathematics, 146. Berlin, Springer-Verlag, 1970. · Zbl 0215.37201 · doi:10.1007/BFb0060932 [2] W. Blaschke and K. Leichtweiss : Elementare Differentialgeometrie , 5 th ed. Berlin, Springer-Verlag, 1973. · Zbl 0264.53001 · eudml:203476 [3] W. Blaschke and G. Bol : Geometrie der Gewebe . Berlin, Springer-Verlag, 1938. · Zbl 0020.06701 · eudml:203712 [4] G. Darboux : Leçons sur la Théorie Générale des Surfaces , 2nd ed. Paris, Gauthier-Villars, 1914. · JFM 45.0881.04 [5] J. Eiesland : On a Certain Class of Algebraic Translation Surfaces . Amer. J. Math. 29 (1908) 363-386. · JFM 38.0642.04 [6] J. Eiesland : On Translation Surfaces Connected with a Unicursal Quartic . Amer. J. Math. 30 (1909) 170-208. · JFM 39.0691.01 [7] J. Fay : Theta Functions on Riemann Surfaces. Lecture Notes in Mathematics 352 . Berlin, Springer-Verlag, 1973. · Zbl 0281.30013 · doi:10.1007/BFb0060090 [8] P. Griffiths : Variations on a Theorem of Abel . Inv. Math. 35 (1976) 321-390. · Zbl 0339.14003 · doi:10.1007/BF01390145 · eudml:142412 [9] T. Jambois : The Theorem of Torelli for Singular Curves . Transactions of the A.M.S. 239 (1978) 123-146. · Zbl 0444.14022 · doi:10.2307/1997850 [10] D. Mumford : Curves and their Jacobians . Ann Arbor, University of Michigan Press, 1975. · Zbl 0316.14010 [11] H. Poincaré : Sur les Surfaces de Translation et les Fonctions Abéliennes . Bull. Soc. Math. de France 29 (1901) 61-86. · JFM 32.0459.04 · www.numdam.org [12] H. Poincaré : Remarques Diverses sur les Fonctions Abéliennes . J. de Math. (Liouville), 5th Series, 1 (1895) 219-314. · JFM 26.0510.01 [13] M. Rosenlicht : Equivalence Relations on Algebraic Curves . Annals of Math. 56 (1952) 169-191. · Zbl 0047.14503 · doi:10.2307/1969773 [14] M. Rosenlicht : Generalized Jacobian Varieties . Annals of Math. 59 (1954) 505-530. · Zbl 0058.37002 · doi:10.2307/1969715 [15] B. Saint-Donat : Variétés de Translation et Théoreme de Torelli . Comptes Rendus Series A 280 (1975) 1611-1612. · Zbl 0304.14022 [16] G. Scheffers : Das Abel’sche Theorem und das Lie’sche Theorem über Translationsflachen . Acta Math. 28 (1904) 65-91. · JFM 35.0426.01 [17] J.-P. Serre : Groupes Algebriques et Crops de Classes . Paris, Hermann, 1959. · Zbl 0097.35604 [18] W. Wirtinger : Lies Translationsmannigfaltigkeiten und Abel’sche Integrale . Monatshefte für Math. und Phys. 46 (1938) 384-431. · Zbl 0019.18204 · doi:10.1007/BF01792693 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.