Let L be a line bundle on a smooth curve C, which defines a birational morphism f C onto f(C). We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo’s curves, a generic section in 2L can be written as a^2 +b^2+c^2 with a, b, c section of L. If there are no quadrics of rank 3 containing f(C) this is true for any section. For canonical curves, this gives a non linear version of Noether’s Theorem.
A non linear version of Noether's type theorem.
BRIVIO, SONIA;PIROLA, GIAN PIETRO
2004-01-01
Abstract
Let L be a line bundle on a smooth curve C, which defines a birational morphism f C onto f(C). We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo’s curves, a generic section in 2L can be written as a^2 +b^2+c^2 with a, b, c section of L. If there are no quadrics of rank 3 containing f(C) this is true for any section. For canonical curves, this gives a non linear version of Noether’s Theorem.File in questo prodotto:
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