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A generalization of Max Noether's theorem


Author: Renato Vidal Martins
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
Published electronically: May 31, 2011
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Abstract: Max Noether's theorem asserts that if $ \omega$ is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve, then the natural morphisms 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.


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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

DOI: https://doi.org/10.1090/S0002-9939-2011-10904-3
Keywords: Singular curve, non-Gorenstein curve, Max Noether theorem
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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