Abstract
Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ⊂ P r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H 0(C, L 2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H 0(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.
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Acknowledgment
Partially supported by (1) PRIN 2003: Spazi di moduli e teoria di Lie. (Murst); (2) Gnsaga; (3) Far 2002 (Pavia): Varietà algebriche, calcolo algebrico, grafi orientati e topologici.
Notes
#Communicated by L. Ein.