Let L be a line bundle on a smooth curve C, which defines a birational morphism onto φ(C) ⊂ Pr. We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H0(C, L2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H0(C, L). If there are no quadrics of rank 3 containing φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem. Copyright © 2004 by Marcel Dekker, Inc.
Brivio, S., Pirola, G. (2004). A nonlinear version of Noether's type Theorem. COMMUNICATIONS IN ALGEBRA, 32(7), 2723-2732 [10.1081/AGB-120037412].
A nonlinear version of Noether's type Theorem
Brivio, S;
2004
Abstract
Let L be a line bundle on a smooth curve C, which defines a birational morphism onto φ(C) ⊂ Pr. We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H0(C, L2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H0(C, L). If there are no quadrics of rank 3 containing φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem. Copyright © 2004 by Marcel Dekker, Inc.
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