Rees algebras of the second syzygy module of the residue field of a regular local ring. (English) Zbl 1191.13030
Ghorpade, Sudhir (ed.) et al., Commutative algebra and algebraic geometry. Joint international meeting of the American Mathematical Society and the Indian Mathematical Society, Bangalore, India, December 17–20, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3629-3/pbk). Contemporary Mathematics 390, 97-108 (2005).
Summary: Let \((A,\mathfrak m)\) be a regular local ring and let \(M\subseteq F=A^d\) be the second syzygy module of the residue field. We introduce the concept of generalized Grassmann algebras and investigate the Rees algebra \(R(M)\) of \(M\). We explore the propertie of generalized Grassmann algebras and prove that the Rees algebra \(R(M)\) of the second syzygy module \(M\) is a Gorenstein factorial domain.
For the entire collection see [Zbl 1078.14001].
For the entire collection see [Zbl 1078.14001].
MSC:
| 13F50 | Rings with straightening laws, Hodge algebras |
| 13A30 | Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics |
| 13D02 | Syzygies, resolutions, complexes and commutative rings |
