On pythagorean real irreducible algebroid curves
In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two...
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| Format: | article |
| Publication Date: | 1984 |
| Country: | España |
| Institution: | Universidad Complutense de Madrid (UCM) |
| Repository: | Docta Complutense |
| Language: | English |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/64761 |
| Online Access: | https://hdl.handle.net/20.500.14352/64761 |
| Access Level: | Open access |
| Keyword: | 512.7 Real irreducible algebroid curve Pythagoras number sum of squares low multiplicity Geometria algebraica 1201.01 Geometría Algebraica |
| Summary: | In this note we deal with the pythagoras number p of certain 1-dimensional rings, i.e., real irreducible algebroid curves over a real closed ground field k. The problem we are concerned with is to characterize those real irreducible algebroid curves which are pythagorean (i.e., p = 1). We obtain two theorems involving the value-semigroup. Then we apply them to solve the cases of: (a) Gorenstein curves, (b) planar curves, (c) monomial curves, and (d) curves of multiplicity <= 5. Finally, two conjectures are stated. |
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