Koszul homology of codimension 3 Gorenstein ideals
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- by Steven V Sam and Jerzy Weyman PDF
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Abstract:
In this note, we calculate the Koszul homology of the codimension 3 Gorenstein ideals. We find filtrations for the Koszul homology in terms of modules with pure free resolutions and completely describe these resolutions. We also consider the Huneke–Ulrich deviation 2 ideals.References
- Lâcezar Avramov and Jürgen Herzog, The Koszul algebra of a codimension $2$ embedding, Math. Z. 175 (1980), no. 3, 249–260. MR 602637, DOI 10.1007/BF01163026
- David A. Buchsbaum and David Eisenbud, Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension $3$, Amer. J. Math. 99 (1977), no. 3, 447–485. MR 453723, DOI 10.2307/2373926
- David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960, DOI 10.1007/978-1-4612-5350-1
- David Eisenbud, Daniel Erman, and Frank-Olaf Schreyer, Filtering free resolutions, Compos. Math. 149 (2013), no. 5, 754–772. MR 3069361, DOI 10.1112/S0010437X12000760
- Daniel R. Grayson, Michael E. Stillman, Macaulay2, a software system for research in algebraic geometry, available at http://www.math.uiuc.edu/Macaulay2/.
- Craig Huneke, Linkage and the Koszul homology of ideals, Amer. J. Math. 104 (1982), no. 5, 1043–1062. MR 675309, DOI 10.2307/2374083
- Craig Huneke, Strongly Cohen-Macaulay schemes and residual intersections, Trans. Amer. Math. Soc. 277 (1983), no. 2, 739–763. MR 694386, DOI 10.1090/S0002-9947-1983-0694386-5
- Andrew R. Kustin, The minimal free resolutions of the Huneke-Ulrich deviation two Gorenstein ideals, J. Algebra 100 (1986), no. 1, 265–304. MR 839583, DOI 10.1016/0021-8693(86)90078-5
- Jerzy Weyman, Cohomology of vector bundles and syzygies, Cambridge Tracts in Mathematics, vol. 149, Cambridge University Press, Cambridge, 2003. MR 1988690, DOI 10.1017/CBO9780511546556
Additional Information
- Steven V Sam
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- Address at time of publication: Department of Mathematics, University of California, Berkeley, California 94704
- MR Author ID: 836995
- ORCID: 0000-0003-1940-9570
- Email: svs@math.berkeley.edu
- Jerzy Weyman
- Affiliation: Department of Mathematics, Northeastern University, Boston, Massachusetts 02115
- Address at time of publication: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
- MR Author ID: 182230
- ORCID: 0000-0003-1923-0060
- Email: j.weyman@neu.edu
- Received by editor(s): March 23, 2012
- Published electronically: October 30, 2013
- Communicated by: Harm Derksen
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 401-408
- MSC (2010): Primary 13D02
- DOI: https://doi.org/10.1090/S0002-9939-2013-12065-4
- MathSciNet review: 3133982