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- W4293368669 abstract "Let $K$ be an algebraically closed field of characteristic $0$, and let $A$ be an Artinian Gorenstein local commutative and Noetherian $K$--algebra, with maximal ideal $M$. In the present paper we prove a structure theorem describing such kind of $K$--algebras satisfying $M^4=0$. We use this result in order to prove that such a $K$--algebra $A$ has rational Poincar'e series and it is always smoothable in any embedding dimension, if $dim_K M^2/M^3 le 4$. We also prove that the generic Artinian Gorenstein local $K$--algebra with socle degree three has rational Poincar'e series, in spite of the fact that such algebras are not necessarily smoothable." @default.
- W4293368669 created "2022-08-28" @default.
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- W4293368669 date "2010-05-10" @default.
- W4293368669 modified "2023-09-27" @default.
- W4293368669 title "Poincar'e series and deformations of Gorenstein local algebras with low socle degree" @default.
- W4293368669 doi "https://doi.org/10.48550/arxiv.1005.1677" @default.
- W4293368669 hasPublicationYear "2010" @default.
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