1-2-3 theorem for curves on algebraic surfaces (Q2710298)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 1-2-3 theorem for curves on algebraic surfaces |
scientific article |
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1-2-3 theorem for curves on algebraic surfaces (English)
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24 April 2001
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canonical ring of 1-connected curves
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Miles Reid's 1-2-3 conjecture
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It is shown that the canonical ring of 1-connected curves on a non-singular surface is generated by its elements of degrees at most three. Furthermore, the relative canonical algebra for pencils of curves is studied to give an answer to Miles Reid's 1-2-3 conjecture that it is generated in degrees at most three. It turns out that the conjecture is true except in only one case, and that the ring is generated in degrees at most four in general.
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