Frames and degenerations of monomial resolutions
HTML articles powered by AMS MathViewer
- by Irena Peeva and Mauricio Velasco
- Trans. Amer. Math. Soc. 363 (2011), 2029-2046
- DOI: https://doi.org/10.1090/S0002-9947-2010-04980-3
- Published electronically: October 25, 2010
- PDF | Request permission
Abstract:
We study free resolutions of monomial ideals in a polynomial ring.References
- E. Batzies and V. Welker, Discrete Morse theory for cellular resolutions, J. Reine Angew. Math. 543 (2002), 147–168. MR 1887881, DOI 10.1515/crll.2002.012
- Dave Bayer, Irena Peeva, and Bernd Sturmfels, Monomial resolutions, Math. Res. Lett. 5 (1998), no. 1-2, 31–46. MR 1618363, DOI 10.4310/MRL.1998.v5.n1.a3
- Dave Bayer and Bernd Sturmfels, Cellular resolutions of monomial modules, J. Reine Angew. Math. 502 (1998), 123–140. MR 1647559, DOI 10.1515/crll.1998.083
- Timothy B. P. Clark, Poset resolutions and lattice-linear monomial ideals, J. Algebra 323 (2010), no. 4, 899–919. MR 2578585, DOI 10.1016/j.jalgebra.2009.11.029
- 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
- Shalom Eliahou and Michel Kervaire, Minimal resolutions of some monomial ideals, J. Algebra 129 (1990), no. 1, 1–25. MR 1037391, DOI 10.1016/0021-8693(90)90237-I
- Vesselin Gasharov, Takayuki Hibi, and Irena Peeva, Resolutions of $\mathbf a$-stable ideals, J. Algebra 254 (2002), no. 2, 375–394. MR 1933875, DOI 10.1016/S0021-8693(02)00083-2
- Vesselin Gasharov, Irena Peeva, and Volkmar Welker, The lcm-lattice in monomial resolutions, Math. Res. Lett. 6 (1999), no. 5-6, 521–532. MR 1739211, DOI 10.4310/MRL.1999.v6.n5.a5
- Michael Jöllenbeck and Volkmar Welker, Minimal resolutions via algebraic discrete Morse theory, Mem. Amer. Math. Soc. 197 (2009), no. 923, vi+74. MR 2488864, DOI 10.1090/memo/0923
- J. Mermin: The Eliahou-Kervaire resolution is cellular, preprint.
- Ezra Miller, The Alexander duality functors and local duality with monomial support, J. Algebra 231 (2000), no. 1, 180–234. MR 1779598, DOI 10.1006/jabr.2000.8359
- Gil Kalai, $f$-vectors of acyclic complexes, Discrete Math. 55 (1985), no. 1, 97–99. MR 793634, DOI 10.1016/S0012-365X(85)80024-8
- Alexandre B. Tchernev, Representations of matroids and free resolutions for multigraded modules, Adv. Math. 208 (2007), no. 1, 75–134. MR 2304312, DOI 10.1016/j.aim.2006.02.002
- Mauricio Velasco, Minimal free resolutions that are not supported by a CW-complex, J. Algebra 319 (2008), no. 1, 102–114. MR 2378063, DOI 10.1016/j.jalgebra.2007.10.011
Bibliographic Information
- Irena Peeva
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- MR Author ID: 263618
- Mauricio Velasco
- Affiliation: Department of Mathematics, Cornell University, Ithaca, New York 14853
- Received by editor(s): August 8, 2008
- Received by editor(s) in revised form: June 14, 2009
- Published electronically: October 25, 2010
- © Copyright 2010 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 2029-2046
- MSC (2000): Primary 13F20
- DOI: https://doi.org/10.1090/S0002-9947-2010-04980-3
- MathSciNet review: 2746674