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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)
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