Translation manifolds and the converse of Abel's theorem

John Little

Compositio Mathematica (1983)

  • Volume: 49, Issue: 2, page 147-171
  • ISSN: 0010-437X

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Little, John. "Translation manifolds and the converse of Abel's theorem." Compositio Mathematica 49.2 (1983): 147-171. <http://eudml.org/doc/89608>.

@article{Little1983,
author = {Little, John},
journal = {Compositio Mathematica},
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},
language = {eng},
number = {2},
pages = {147-171},
publisher = {Martinus Nijhoff Publishers},
title = {Translation manifolds and the converse of Abel's theorem},
url = {http://eudml.org/doc/89608},
volume = {49},
year = {1983},
}

TY - JOUR
AU - Little, John
TI - Translation manifolds and the converse of Abel's theorem
JO - Compositio Mathematica
PY - 1983
PB - Martinus Nijhoff Publishers
VL - 49
IS - 2
SP - 147
EP - 171
LA - eng
KW - 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
UR - http://eudml.org/doc/89608
ER -

References

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  2. [2] W. Blaschke and K. Leichtweiss: Elementare Differentialgeometrie, 5 th ed. Berlin, Springer-Verlag, 1973. Zbl0264.53001MR350630
  3. [3] W. Blaschke and G. Bol: Geometrie der Gewebe. Berlin, Springer-Verlag, 1938. Zbl0020.06701JFM64.0727.03
  4. [4] G. Darboux: Leçons sur la Théorie Générale des Surfaces, 2nd ed. Paris, Gauthier-Villars, 1914. JFM45.0881.04
  5. [5] J. Eiesland: On a Certain Class of Algebraic Translation Surfaces. Amer. J. Math.29 (1908) 363-386. Zbl38.0642.04MR1506020JFM38.0642.04
  6. [6] J. Eiesland: On Translation Surfaces Connected with a Unicursal Quartic. Amer. J. Math.30 (1909) 170-208. Zbl39.0691.01MR1506037JFM39.0691.01
  7. [7] J. Fay: Theta Functions on Riemann Surfaces. Lecture Notes in Mathematics 352. Berlin, Springer-Verlag, 1973. Zbl0281.30013MR335789
  8. [8] P. Griffiths: Variations on a Theorem of Abel. Inv. Math.35 (1976) 321-390. Zbl0339.14003MR435074
  9. [9] T. Jambois: The Theorem of Torelli for Singular Curves. Transactions of the A.M.S. 239 (1978) 123-146. Zbl0444.14022MR498584
  10. [10] D. Mumford: Curves and their Jacobians. Ann Arbor, University of Michigan Press, 1975. Zbl0316.14010MR419430
  11. [11] H. Poincaré: Sur les Surfaces de Translation et les Fonctions Abéliennes. Bull. Soc. Math. de France29 (1901) 61-86. Zbl32.0459.04MR1504382JFM32.0459.04
  12. [12] H. Poincaré: Remarques Diverses sur les Fonctions Abéliennes. J. de Math. (Liouville), 5th Series, 1 (1895) 219-314. Zbl26.0510.01JFM26.0510.01
  13. [13] M. Rosenlicht: Equivalence Relations on Algebraic Curves. Annals of Math. 56 (1952) 169-191. Zbl0047.14503MR48856
  14. [14] M. Rosenlicht: Generalized Jacobian Varieties. Annals of Math. 59 (1954) 505-530. Zbl0058.37002MR61422
  15. [15] B. Saint-Donat: Variétés de Translation et Théoreme de Torelli. Comptes Rendus Series A280 (1975) 1611-1612. Zbl0304.14022MR469925
  16. [16] G. Scheffers: Das Abel'sche Theorem und das Lie'sche Theorem über Translationsflachen. Acta Math. 28 (1904) 65-91. JFM35.0426.01
  17. [17] J.-P. Serre: Groupes Alge{briques et Crops de Classes. Paris, Hermann, 1959. Zbl0097.35604
  18. [18] W. Wirtinger: Lies Translationsmannigfaltigkeiten und Abel'sche Integrale. Monatshefte für Math. und Phys. 46 (1938) 384-431. Zbl0019.18204JFM64.1337.02

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