Generalization of a Max Noether’s Theorem
نویسنده
چکیده
Max Noether’s Theorem asserts that if ω is the dualizing sheaf of a nonsingular nonhyperelliptic projective curve then the natural morphisms SymH(ω) → H(ω) are surjective for all n ≥ 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.
منابع مشابه
Adjoints and Max Noether’s Fundamentalsatz
We give an exposition of the theory of adjoints and conductors for curves on nonsingular surfaces, emphasizing the case of plane curves, for which the presentation is particularly elementary. This is closely related to Max Noether’s “AF +BG” theorem, which is proved for curves with arbitrary multiple components.
متن کاملExtensions of Noether’s Second Theorem: from continuous to discrete systems
A simple local proof of Noether’s Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler–Lagrange equations of any variational problem whose symmetries depend upon a set of free or partly-constrained functions. Our approach extends further to deal with finite difference systems. The res...
متن کاملBézout’s Theorem for Curves
The goal of this paper is to prove Bézout’s Theorem for algebraic curves. Along the way, we introduce some basic notions in algebraic geometry such as affine and projective varieties and intersection numbers of algebraic curves. After proving Bézout’s Theorem, we investigate Max Noether’s Fundamental Theorem and construct the group law on a plane cubic which is the first step in studying the ar...
متن کاملA ug 2 00 9 EXPLICIT REPRESENTATION OF MEMBERSHIP IN POLYNOMIAL
We introduce a new division formula on projective space which provides explicit solutions to various polynomial division problems with sharp degree estimates. We consider simple examples as the classical Macaulay theorem as well as a quite recent result by Hickel, related to the effective Nullstellensatz. We also obtain a related result that generalizes Max Noether’s classical AF + BG theorem.
متن کاملGeneralization of Titchmarsh's Theorem for the Dunkl Transform
Using a generalized spherical mean operator, we obtain a generalization of Titchmarsh's theorem for the Dunkl transform for functions satisfying the ('; p)-Dunkl Lipschitz condition in the space Lp(Rd;wl(x)dx), 1 < p 6 2, where wl is a weight function invariant under the action of an associated re ection group.
متن کامل