2017/05/03 by H. Ananthnarayan, Ananthnarayan, H., Ela Celikbas +5 · 1 citation
Mathematics · #13A30 #13D40 #13H10 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1705.01413
openalex publication_date 2017/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In 2012, Ananthnarayan, Avramov and Moore gave a new construction of Gorenstein rings from two Gorenstein local rings, called their connected sum. In this article, we investigate conditions on the associated graded ring of a Gorenstein Artin local ring Q, which force it to be a connected sum over its residue field. In particular, we recover some results regarding short, and stretched, Gorenstein Artin rings. Finally, using these decompositions, we obtain results about the rationality of the Poincare series of Q.