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REGULARITY OF REES ALGEBRAS

  • JÜRGEN HERZOG (a1), DORIN POPESCU (a2) and NGÔ VIÊT TRUNG (a3)
Abstract

Let $B = k[x_1, \ldots, x_n]$ be a polynomial ring over a field $k$ , and let $A$ be a quotient ring of $B$ by a homogeneous ideal $J$ . Let $\frak{m}$ denote the maximal graded ideal of $A$ . Then the Rees algebra $R = A[{\frak{m}} t]$ also has a presentation as a quotient ring of the polynomial ring $k[x_1, \ldots, x_n, y_1, \ldots, y_n]$ by a homogeneous ideal $J^*$ . For instance, if $A = k[x_1, \ldots, x_n]$ , then \[ R \cong k[x_1, \ldots, x_n, y_1, \ldots, y_n]/(x_i y_j - x_j y_i\mid i,j = 1, \ldots, n). \] In this paper we want to compare the homological properties of the homogeneous ideals $J$ and $J^*$ .

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Journal of the London Mathematical Society
  • ISSN: 0024-6107
  • EISSN: 1469-7750
  • URL: /core/journals/journal-of-the-london-mathematical-society
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