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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Abel's theorem for twisted Jacobians

Authors: Donu Arapura and Kyungho Oh
Journal: Trans. Amer. Math. Soc. 342 (1994), 421-433
MSC: Primary 14C30; Secondary 14H40
MathSciNet review: 1162101
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Abstract: A twisted version of the Abel-Jacobi map, associated to a local system with finite monodromy on a smooth projectve complex curve, is introduced. An analogue of Abel's theorem characterizing the kernel of this map is proved. The proof, which is new even in the classical case, involves reinterpreting the Abel-Jacobi map in the language of mixed Hodge structures and their extensions.

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  • [B] A. Borel et al., Algebraic D-modules, Academic Press, 1987. MR 882000 (89g:32014)
  • [C] J. Carlson, Extensions of mixed Hodge structures, Journées de Géométrie Algébrique d'Angers 1979, Sijthoff & Noordhoff, 1980, pp. 107-127. MR 605338 (82g:14013)
  • [D] P. Deligne, Théorie de Hodge II, III, Publ. Inst. Hautes Études Sci. 40 (1972), 5-57; 44 (1974), 5-77. MR 0498551 (58:16653a)
  • [GH] P. A. Griffiths and J. Harris, Principles of algebraic geometry, Wiley, 1978. MR 507725 (80b:14001)
  • [Z] S. Zucker, Hodge theory with degenerating coefficients: $ {L_2}$ cohomology in the Poincaré metric. Ann. of Math. 109 (1979), 415-476 MR 534758 (81a:14002)

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