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Transactions of the American Mathematical Society

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

 

 

Theta-characteristics on algebraic curves


Author: Joe Harris
Journal: Trans. Amer. Math. Soc. 271 (1982), 611-638
MSC: Primary 14H99; Secondary 14C20, 14K25
MathSciNet review: 654853
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Abstract: The theory of theta-characteristics is developed algebraically, so that it may be applied to possibly singular and/or reducible algebraic curves. The configuration of theta-characteristics on a curve is described in terms of its singularities, with applications to the geometry of plane quartic curves and the problem of Appolonius. Some results on Gorenstein local rings are appended.


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  • [1] H. F. Baker, Principles of geometry, Vol. IV, Chapter II; Cambridge Univ. Press, 1925.
  • [2] E. Griffin, Thesis, Harvard Univ., Cambridge, Mass., 1982.
  • [3] Phillip Griffiths and Joseph Harris, Principles of algebraic geometry, Wiley-Interscience [John Wiley & Sons], New York, 1978. Pure and Applied Mathematics. MR 507725
  • [4] H. Hilton, Plane algebraic curves, Oxford, 1920.
  • [5] Joe Harris, Galois groups of enumerative problems, Duke Math. J. 46 (1979), no. 4, 685–724. MR 552521
  • [6] Heisuke Hironaka, On the arithmetic genera and the effective genera of algebraic curves, Mem. Coll. Sci. Univ. Kyoto. Ser. A. Math. 30 (1957), 177–195. MR 0090850
  • [7] Serge Lang, On quasi algebraic closure, Ann. of Math. (2) 55 (1952), 373–390. MR 0046388
  • [8 D] David Mumford, Theta characteristics of an algebraic curve, Ann. Sci. École Norm. Sup. (4) 4 (1971), 181–192. MR 0292836
  • [9] G. Salmon, Conic sections, Longman, Greens & Co., London, 1879.
  • [10] -, Higher plane curves, Hodges, Foster & Co., Dublin, 1879.
  • [11] C. T. C. Wall, Nets of quadrics, and theta-characteristics of singular curves, Philos. Trans. Roy. Soc. London Ser. A 289 (1978), no. 1357, 229–269. MR 0506258

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DOI: https://doi.org/10.1090/S0002-9947-1982-0654853-6
Article copyright: © Copyright 1982 American Mathematical Society