×

Almost Gorenstein determinantal rings of symmetric matrices. (English) Zbl 1497.13043

Summary: We provide a characterization of the almost Gorenstein property of determinantal rings of a symmetric matrix of indeterminates over an infinite field. We give an explicit formula for ranks of the last two modules in the resolution of determinantal rings using Schur functors.

MSC:

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13H15 Multiplicity theory and related topics
13D02 Syzygies, resolutions, complexes and commutative rings
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Barile, M., The Cohen-Macaulayness and the a-invariant of an algebra with straightening laws on a doset, Commun. Algebra, 22, 2, 413-430 (1994) · Zbl 0840.13012 · doi:10.1080/00927879408824858
[2] Barucci, V.; Fröberg, R., One-dimensional almost Gorenstein rings, J. Algebra, 188, 2, 418-442 (1997) · Zbl 0874.13018 · doi:10.1006/jabr.1996.6837
[3] Boffi, G.; Sánchez, R., On the resolutions of the powers of the Pfaffian ideals, J. Algebra, 152, 2, 463-491 (1992) · Zbl 0787.13009 · doi:10.1016/0021-8693(92)90044-M
[4] Conca, A., Symmetric ladders, Nagoya Math. J, 136, 35-56 (1994) · Zbl 0810.13010 · doi:10.1017/S0027763000024958
[5] De Concini, C.; Procesi, C., A characteristic free approach to invariant theory, Adv. Math, 21, 3, 330-354 (1976) · Zbl 0347.20025 · doi:10.1016/S0001-8708(76)80003-5
[6] Goto, S., On the Gorensteinness of determinantal loci, J. Math. Kyoto Univ, 19, 371-374 (1979) · Zbl 0418.13008
[7] Goto, S.; Matsuoka, N.; Phuong, T. T., Almost Gorenstein rings, J. Algebra, 379, 263-278 (2013)
[8] Goto, S.; Matsuoka, N.; Taniguchi, N.; Yoshida, K.-I., The almost Gorenstein Rees algebras of parameters, J. Algebra, 452, 263-278 (2016) · Zbl 1338.13042 · doi:10.1016/j.jalgebra.2015.12.022
[9] Goto, S.; Takahashi, R.; Taniguchi, N., Almost Gorenstein rings towards a theory of higher dimension, J. Pure Appl. Algebra, 219, 7, 2666-2712 (2015) · Zbl 1319.13017 · doi:10.1016/j.jpaa.2014.09.022
[10] Kutz, R. E., Cohen-Macaulay rings and ideal theory in rings of invariants of algebraic groups, Trans. Amer. Math. Soc, 194, 115-129 (1974) · Zbl 0288.13004 · doi:10.1090/S0002-9947-1974-0352082-2
[11] Perlman, M., Regularity and cohomology of Pfaffian thickenings, J0. Commun. Algebra · Zbl 1496.13027
[12] Stanley, R. P., Hilbert functions of graded algebras, Adv. Math, 28, 1, 57-83 (1978) · Zbl 0384.13012 · doi:10.1016/0001-8708(78)90045-2
[13] Taniguchi, N., On the almost Gorenstein property of determinantal rings, Commun. Algebra, 46, 3, 1165-1178 (2018) · Zbl 1400.13025 · doi:10.1080/00927872.2017.1339066
[14] Weyman, J., Cohomology of Vector Bundles and Syzygies (2003), Cambridge, MA: Cambridge University Press, Cambridge, MA · Zbl 1075.13007
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.