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.
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Titolo: | A non linear version of Noether's type theorem. | |
Autori: | ||
Data di pubblicazione: | 2004 | |
Rivista: | ||
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. | |
Handle: | http://hdl.handle.net/11571/132870 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |
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