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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A generalization of Max Noether’s theorem
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by Renato Vidal Martins PDF
Proc. Amer. Math. Soc. 140 (2012), 377-391 Request permission

Abstract:

Max Noether’s theorem asserts that if $\omega$ is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms $\text {Sym}^nH^0(\omega )\to H^0(\omega ^n)$ are surjective for all $n\geq 1$. This is true for Gorenstein nonhyperelliptic curves as well. We prove that this remains true for nearly Gorenstein curves and for all integral nonhyperelliptic curves whose non-Gorenstein points are unibranch. The results are independent and have different proofs. The first one is extrinsic, the second intrinsic.
References
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Additional Information
  • Renato Vidal Martins
  • Affiliation: Departamento de Matemática, Instituto de Ciencias Exatas, Universidade Federal de Minas Gerais, Av. Antônio Carlos 6627, 30123-970 Belo Horizonte MG, Brazil
  • Email: renato@mat.ufmg.br
  • Received by editor(s): September 14, 2009
  • Received by editor(s) in revised form: November 16, 2010
  • Published electronically: May 31, 2011
  • Communicated by: Bernd Ulrich
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 140 (2012), 377-391
  • MSC (2010): Primary 14H20; Secondary 14H45, 14H51
  • DOI: https://doi.org/10.1090/S0002-9939-2011-10904-3
  • MathSciNet review: 2846308