대한수학회지 (Journal of the Korean Mathematical Society)

  • 제53권2호
  • /
  • Pages.263-286
  • /
  • 2016
  • /
  • 0304-9914(pISSN)
  • /
  • 2234-3008(eISSN)
대한수학회 (Korean Mathematical Society)
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GALOIS COVERINGS AND JACOBI VARIETIES OF COMPACT RIEMANN SURFACES

  • 투고 : 2014.11.17
  • 발행 : 2016.03.01
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초록

We discuss relations between Galois coverings of compact Riemann surfaces and their Jacobi varieties. We prove a theorem of a kind of Galois correspondence for Abelian subvarieties of Jacobi varieties. We also prove a theorem on the sets of points in Jacobi varieties fixed by Galois group actions.

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참고문헌

  1. R. D. M. Accola, Riemann Surfaces, Theta Functions and Abelian Automorphism Groups, Lecture Notes in Mathematics, Vol. 483. Springer-Verlag, Berlin-New York, 1975.
  2. M. Namba, Equivalence problem and automorphism groups of certain compact Riemann surfaces, Tsukuba J. Math. 5 (1981), no. 2, 319-338. https://doi.org/10.21099/tkbjm/1496159409
  3. M. Namba, Geometry of Projective Algebraic Curves, Marcel Dekker, 1984.
  4. L. S. Pontryagin, Topological Groups, Translated from the second Russian edition by Arlen Brown Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966.