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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Let ![$ R=\mathbbm{k}[x_1,\ldots, x_n]$](/proc/2011-139-07/S0002-9939-2010-10677-9/gif-abstract0/img1.gif){kind=small}
and let 
be a multigraded squarefree module. We discuss the construction of cochain complexes associated to 
and we show how to interpret homological invariants of 
in terms of topological computations. This is a generalization of the well-studied case of squarefree monomial ideals.
- [BrHe95] Winfried Bruns and Jürgen Herzog, On multigraded resolutions, Math. Proc. Cambridge Philos. Soc. 118 (1995), no. 2, 245–257. MR 1341789, https://doi.org/10.1017/S030500410007362X
- [BrHe98] Winfried Bruns and Jürgen Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993. MR 1251956
- [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] Hara Charalambous and Christa Deno, Multigraded modules, New York J. Math. 7 (2001), 1–6. MR 1817761
- [ChTc03] 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, https://doi.org/10.4310/MRL.2003.v10.n4.a12
- [Ei97] David Eisenbud, Commutative algebra, Graduate Texts in Mathematics, vol. 150, Springer-Verlag, New York, 1995. With a view toward algebraic geometry. MR 1322960
- [Ho77] Melvin Hochster, Cohen-Macaulay rings, combinatorics, and simplicial complexes, Ring theory, II (Proc. Second Conf., Univ. Oklahoma, Norman, Okla., 1975), Dekker, New York, 1977, pp. 171–223. Lecture Notes in Pure and Appl. Math., Vol. 26. MR 0441987
- [MiSt05] Ezra Miller and Bernd Sturmfels, Combinatorial commutative algebra, Graduate Texts in Mathematics, vol. 227, Springer-Verlag, New York, 2005. MR 2110098
- [St83] Richard P. Stanley, Combinatorics and commutative algebra, Progress in Mathematics, vol. 41, Birkhäuser Boston, Inc., Boston, MA, 1983. MR 725505
- [Ya00] Kohji Yanagawa, Alexander duality for Stanley-Reisner rings and squarefree 𝐍ⁿ-graded modules, J. Algebra 225 (2000), no. 2, 630–645. MR 1741555, https://doi.org/10.1006/jabr.1999.8130
-graded modules. J. Algebra, 225 (2000), 630-645. Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13C15, 13D02, 13D45
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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.
