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Poincaré Series and Deformations of Gorenstein Local Algebras

Communications in Algebra, ISSN: 0092-7872, Vol: 41, Issue: 3, Page: 1049-1059
2013
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Metrics Details

  • Citations
    10
    • Citation Indexes
      10
  • Captures
    2

Article Description

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 m = 0. We use this result in order to prove that such a K-algebra has rational Poincaré series and it is smoothable in any embedding dimension, provided dim m/m ≤ 4. We also prove that the generic Artinian Gorenstein local K-algebra with m = 0 has rational Poincaré series. © 2013 Copyright Taylor and Francis Group, LLC.

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