Generalization of a Max Noether's Theorem

Details Generalization of a Max Noether's Theorem Generalization of a Max Noether's Theorem

2009-08-17

arxiv.org/abs/0908.2410v1

Mathematics

Algebraic Geometry

Scientific paper

Max Noether's Theorem asserts that if $\ww$ 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 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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