Vanishing of Tor modules and homological dimensions of unions of aCM schemes. (English) Zbl 1113.13008
This paper discusses the vanishing of Tor modules and homological dimensions of unions of unions of aCM schemes. In particular, the authors give some generalization when one of the two schemes has codimension 2 and apply this result to the monomial case. The reviewer thinks it is important and useful for the study of homological dimensions.
Reviewer: Zhan Jianming (Enshi)
MSC:
| 13D07 | Homological functors on modules of commutative rings (Tor, Ext, etc.) |
References:
| [1] | Buchsbaum, D. A.; Eisenbud, D., What makes a complex exact?, J. Algebra, 25, 259-268 (1973) · Zbl 0264.13007 |
| [2] | Eisenbud, D., Commutative Algebra with a View Toward Algebraic Geometry, Grad. Texts in Math., vol. 150 (1996), Springer-Verlag |
| [3] | Herzog, J.; Takayama, Y.; Terai, N., On the radical of a monomial ideal, Arch. Math. (Basel), 85, 397-408 (2005) · Zbl 1112.13003 |
| [4] | Martin-Deschamps, M.; Perrin, D., Sur la classification des courbes gauches, Astérisque, 184-185 (1990) · Zbl 0717.14017 |
| [5] | Migliore, J., Submodules of the deficiency module, J. London Math. Soc. (2), 48, 396-414 (1993) · Zbl 0790.14041 |
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