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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© 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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