Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system
Let $ K$ be an algebraically closed field of characteristc zero. In this paper we study the isomorphism classes of Artinian Gorenstein local $ K$-algebras with socle degree three by means of Macaulay's inverse system. We prove that their classification is equivalent to the projective classifica...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2012 |
| País: | España |
| Institución: | Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya) |
| Repositorio: | Recercat. Dipósit de la Recerca de Catalunya |
| OAI Identifier: | oai:recercat.cat:2445/96644 |
| Acceso en línea: | https://hdl.handle.net/2445/96644 |
| Access Level: | acceso abierto |
| Palabra clave: | Isomorfismes (Matemàtica) Àlgebra Anells (Àlgebra) Isomorphisms (Mathematics) Algebra Rings (Algebra) |
| Sumario: | Let $ K$ be an algebraically closed field of characteristc zero. In this paper we study the isomorphism classes of Artinian Gorenstein local $ K$-algebras with socle degree three by means of Macaulay's inverse system. We prove that their classification is equivalent to the projective classification of cubic hypersurfaces in $ \mathbb{P}_K ^{n }$. This is an unexpected result because it reduces the study of this class of local rings to the graded case. The result has applications in problems concerning the punctual Hilbert scheme $ \operatorname {Hilb}_d (\mathbb{P}_K^n) $ and in relation to the problem of the rationality of the Poincaré series of local rings. |
|---|