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On the Noether gap theorem

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Part of the Lecture Notes in Mathematics book series (LNM,volume 971)

Abstract

Some of the facts immediately surrounding the Weierstrass Gap Theorem are not true when restated for the Noether Gap Theorem. For example, the sum of two Noether non-gaps need not be a non-gap. On the other hand, like Weierstrass points, Noether sequences form an analytic set of codimension 1. In fact, both can be described as the zero loci of appropriate differentials. In addition, the gap sequences on a hyperelliptic surface are of special type and, for arbitrary surfaces, a "principle of non-degeneracy" holds.

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Bibliography

  1. A. Andreotti, "On a theorem of Torelli," Amer. J. ot Math., 80 (1958), 801–828.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. H.M. Farkas and I. Kra, Riemann Surfaces, Springer, New York, Heidelberg, Berlin, 1980.

    CrossRef  MATH  Google Scholar 

  3. R.C. Gunning, Lectures on Riemann surfaces, Jacobi varieties, Princeton University Press, Princeton, N.J., 1972.

    MATH  Google Scholar 

  4. Th. Meis, "Die minimale Blätterzahl der Konkretisierungen einer kompakten Riemannschen Fläche," Schriftenreiche des Math. Inst., Münster, 1960.

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  5. H.E. Rauch, "Weierstrass points, branch points and moduli of Riemann surfaces," Comm. Pure Appl. Math., 12 (1959), 543–560.

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© 1983 Spring-Verlay

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Engber, M. (1983). On the Noether gap theorem. In: Gallo, D.M., Porter, R.M. (eds) Kleinian Groups and Related Topics. Lecture Notes in Mathematics, vol 971. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067070

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  • DOI: https://doi.org/10.1007/BFb0067070

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11975-3

  • Online ISBN: 978-3-540-39426-6

  • eBook Packages: Springer Book Archive