Quadratic Gorenstein rings and the Koszul property I
Authors:
Matthew Mastroeni, Hal Schenck and Mike Stillman
Journal:
Trans. Amer. Math. Soc. 374 (2021), 1077-1093
MSC (2020):
Primary 13D02; Secondary 14H45, 14H50
DOI:
https://doi.org/10.1090/tran/8214
Published electronically:
November 18, 2020
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let 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
or if
and
, and they ask whether this is true for
in general. We determine sufficient conditions on a non-Koszul quadratic Cohen-Macaulay ring
that guarantee the Nagata idealization
is a non-Koszul quadratic Gorenstein ring. We prove there exist rings of regularity
satisfying our conditions for all
; this yields a negative answer to the question from the above-mentioned paper.
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Additional Information
Matthew Mastroeni
Affiliation:
Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email:
mmastro@okstate.edu
Hal Schenck
Affiliation:
Department of Mathematics, Iowa State University, Ames, Iowa 50011
Email:
hschenck@iastate.edu
Mike Stillman
Affiliation:
Department of Mathematics, Cornell University, Ithaca, New York 14850
Email:
mike@math.cornell.edu
DOI:
https://doi.org/10.1090/tran/8214
Keywords:
Syzygy,
Koszul algebra,
Gorenstein algebra.
Received by editor(s):
August 9, 2019
Received by editor(s) in revised form:
May 2, 2020
Published electronically:
November 18, 2020
Additional Notes:
The second author was supported by NSF Grant 1818646.
The third author was supported by NSF Grant 1502294.
Article copyright:
© Copyright 2020
American Mathematical Society