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Topological constructions for multigraded squarefree modules


Author: Hara Charalambous
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
Published electronically: December 17, 2010
MathSciNet review: 2784803
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Abstract: Let $ R=\mathbbm{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 [Enhancements On Off] (What's this?)

  • [BrHe95] W. BRUNS AND J. HERZOG, On multigraded resolutions, Math. Proc. Camb. Phil. Soc., 118 (1995), 245-257. MR 1341789 (96g:13013)
  • [BrHe98] W. BRUNS AND J. HERZOG, Cohen-Macaulay Rings, Cambridge University Press, 1998. MR 1251956 (95h:13020)
  • [Ch06] H. CHARALAMBOUS, Multigraded Modules and Simplicial complexes, Proceedings of the 6th Panhellenic Conference in Algebra and Number Theory, Aristotle Univ. Thessalonike, 2006, 21-24.
  • [ChDe01] H. CHARALAMBOUS AND C. DENO, Multigraded modules, New York Journal of Mathematics, 7 (2001), 1-6. MR 1817761 (2002a:13009)
  • [ChTc03] H. CHARALAMBOUS AND A. TCHERNEV, Free resolutions for multigraded modules: A generalization of Taylor's construction, Math. Res. Lett., 10 (2003), 535-550. MR 1995792 (2004e:13020)
  • [Ei97] D. EISENBUD, Commutative Algebra with a View toward Algebraic Geometry, Springer Verlag, 1997. MR 1322960 (97a:13001)
  • [Ho77] M. HOCHSTER, Cohen-Macaulay rings, combinatorics, and simplicial complexes, Ring Theory. II, Lect. Notes in Pure and Applied Math., 26, M. Dekker, 1977, 171-223. MR 0441987 (56:376)
  • [MiSt05] E. MILLER AND B. STURMFELS, Combinatorial Commutative Algebra, Graduate Texts in Mathematics, 227, Springer Verlag, 2005. MR 2110098 (2006d:13001)
  • [St83] R. STANLEY, Combinatorics and Commutative Algebra, Birkhäuser, 1983. MR 725505 (85b:05002)
  • [Ya00] K. YANAGAWA, Alexander duality for Stanley-Reisner rings and squarefree $ \mathbf{N}^n$-graded modules. J. Algebra, 225 (2000), 630-645. MR 1741555 (2000m:13036)

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Additional Information

Hara Charalambous
Affiliation: Department of Mathematics, Aristotle University of Greece, Thessaloniki, 54124, Greece
Email: hara@math.auth.gr

DOI: https://doi.org/10.1090/S0002-9939-2010-10677-9
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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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