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A generalization of Max Noether’s theorem. (English) Zbl 1234.14025
Authors’ 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.

##### MSC:
 14H20 Singularities of curves, local rings 14H45 Special algebraic curves and curves of low genus 14H51 Special divisors on curves (gonality, Brill-Noether theory)
##### Keywords:
singular curve; non-Gorenstein curve; Max Noether theorem
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##### References:
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