Topological constructions for multigraded squarefree modules
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Abstract:
Let $R=\mathbb {k}[x_1,\ldots , x_n]$ and let $M=R^s/I$ be a multigraded squarefree module. We discuss the construction of cochain complexes associated to $M$ and we show how to interpret homological invariants of $M$ in terms of topological computations. This is a generalization of the well-studied case of squarefree monomial ideals.References
- Winfried Bruns and Jürgen Herzog, On multigraded resolutions, Math. Proc. Cambridge Philos. Soc. 118 (1995), no. 2, 245–257. MR 1341789, DOI 10.1017/S030500410007362X
- Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- H. Charalambous, Multigraded Modules and Simplicial complexes, Proceedings of the 6th Panhellenic Conference in Algebra and Number Theory, Aristotle Univ. Thessalonike, 2006, 21-24.
- Hara Charalambous and Christa Deno, Multigraded modules, New York J. Math. 7 (2001), 1–6. MR 1817761
- Hara Charalambous and Alexandre Tchernev, Free resolutions for multigraded modules: a generalization of Taylor’s construction, Math. Res. Lett. 10 (2003), no. 4, 535–550. MR 1995792, DOI 10.4310/MRL.2003.v10.n4.a12
- 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
- Melvin Hochster, Cohen-Macaulay rings, combinatorics, and simplicial complexes, Ring theory, II (Proc. Second Conf., Univ. Oklahoma, Norman, Okla., 1975) Lecture Notes in Pure and Appl. Math., Vol. 26, Dekker, New York, 1977, pp. 171–223. MR 0441987
- Ezra Miller and Bernd Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, vol. 227, Springer-Verlag, New York, 2005. MR 2110098
- Richard P. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 725505, DOI 10.1007/978-1-4899-6752-7
- Kohji Yanagawa, Alexander duality for Stanley-Reisner rings and squarefree $\mathbf N^n$-graded modules, J. Algebra 225 (2000), no. 2, 630–645. MR 1741555, DOI 10.1006/jabr.1999.8130
Additional Information
- Hara Charalambous
- Affiliation: Department of Mathematics, Aristotle University of Greece, Thessaloniki, 54124, Greece
- Email: hara@math.auth.gr
- Received by editor(s): August 28, 2009
- Received by editor(s) in revised form: June 30, 2010
- Published electronically: December 17, 2010
- Communicated by: Bernd Ulrich
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 2383-2397
- MSC (2010): Primary 13C15, 13D02, 13D45
- DOI: https://doi.org/10.1090/S0002-9939-2010-10677-9
- MathSciNet review: 2784803