Fitxers
Tipus de document
ArticleVersió
Versió publicadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/96644
Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system
Títol de la revista
Autors
Director/Tutor
ISSN de la revista
Títol del volum
Recurs relacionat
Resum
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.
Matèries
Matèries (anglès)
Citació
Citació
ELÍAS GARCÍA, Joan and ROSSI, M. E. Isomorphism classes of short Gorenstein local rings via Macaulay's inverse system. Transactions of the American Mathematical Society. 2012. Vol. 364, num. 9, pags. 4589-4604. ISSN 0002-9947. [consulted: 25 of June of 2026]. Available at: https://hdl.handle.net/2445/96644