Poincaré Series and Deformations of Gorenstein Local Algebras

Autor:	Roberto Notari, Gianfranco Casnati, Juan Elias, Maria Evelina Rossi
Rok vydání:	2013
Předmět:	Poincarè series Pure mathematics Algebra and Number Theory Mathematics::Commutative Algebra Mathematics::Rings and Algebras Local ring Order (ring theory) Dimension (vector space) Gorenstein rings Poincaré series Embedding Algebraically closed field Structured program theorem Mathematics
Zdroj:	Communications in Algebra. 41:1049-1059
ISSN:	1532-4125 0092-7872
DOI:	10.1080/00927872.2011.636643
Popis:	Let (A, 𝔪, K) be an Artinian Gorenstein local ring with K an algebraically closed field of characteristic 0. In the present article, we prove a structure theorem describing the Artinian Gorenstein local K-algebras satisfying 𝔪4 = 0. We use this result in order to prove that such a K-algebra has rational Poincare series and it is smoothable in any embedding dimension, provided dim K 𝔪2/𝔪3 ≤ 4. We also prove that the generic Artinian Gorenstein local K-algebra with 𝔪4 = 0 has rational Poincare series.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb1b7055baca58b50caa2df566340a3b https://doi.org/10.1080/00927872.2011.636643 Zobrazit plný text záznamu