1. Quadratic Gorenstein rings and the Koszul property I.
- Author
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Mastroeni, Matthew, Schenck, Hal, and Stillman, Mike
- Subjects
GORENSTEIN rings ,COHEN-Macaulay rings ,KOSZUL algebras ,ALGEBRA ,MATHEMATICS - Abstract
Let R be a standard graded Gorenstein algebra over a field presented by quadrics. In [Compositio Math. 129 (2001), no. 1, 95-121], Conca-Rossi-Valla show that such a ring is Koszul if reg R ≤ 2 or if reg R = 3 and c = codim R ≤ 4, and they ask whether this is true for reg R = 3 in general. We determine sufficient conditions on a non-Koszul quadratic Cohen-Macaulay ring R that guarantee the Nagata idealization ~ R = R × ω
R (−a−1) is a non-Koszul quadratic Gorenstein ring. We prove there exist rings of regularity 3 satisfying our conditions for all c ≥ 9; this yields a negative answer to the question from the above-mentioned paper. [ABSTRACT FROM AUTHOR]- Published
- 2021
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