A generalization of Max Noether’s theorem
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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 $\text {Sym}^nH^0(\omega )\to H^0(\omega ^n)$ 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