A class of noncommutative projective surfaces
A class of noncommutative projective surfaces
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一类非交换射影曲面
DOI：
10.1112/plms/pdn054
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发表时间：
2006
影响因子：
1.8
通讯作者：
J. T. Stafford
中科院分区：
文献类型：
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作者：
D. Rogalski;J. T. Stafford
设A = ⊕I⩾0Ai是代数闭域k上一次生成的连通分次Notherian k-代数，设分次商环Q(A)的形式为Q(A) = k(X)[t，t−1；σ]，其中σ是积分射影曲面X的自同构，那么我们证明了A可以表示为射影曲面的朴素爆破代数？这使得人们能够对这些代数的结构有一个深刻的了解；例如，它们一般不是强Notherian的，它们的点模也不是由射影方案参数化的。这是尽管QGR-A中的简单对象将总是与方案的闭合点？(1-1)对应。
Let A = ⊕i⩾0Ai be a connected graded, noetherian k‐algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A) = k(X)[t, t−1; σ], where σ is an automorphism of the integral projective surface X. Then we prove that A can be written as a naïve blowup algebra of a projective surface ? birational to X. This enables one to obtain a deep understanding of the structure of these algebras; for example, generically they are not strongly noetherian and their point modules are not parametrized by a projective scheme. This is despite the fact that the simple objects in qgr‐A will always be in (1‐1) correspondence with the closed points of the scheme ?.