ar X iv : m at h / 04 01 09 8 v 2 [ m at h . R A ] 3 1 M ay 2 00 5 PROJECTIVELY SIMPLE RINGS
نویسنده
چکیده
An infinite-dimensional N-graded k-algebra A is called projectively simple if dimk A/I < ∞ for every nonzero two-sided ideal I ⊂ A. We show that if a projectively simple ring A is strongly noetherian, is generated in degree 1, and has a point module, then A is equal in large degree to a twisted homogeneous coordinate ring B = B(X,L, σ). Here X is a smooth projective variety, σ is an automorphism of X with no proper σ-invariant subvariety (we call such automorphisms wild), and L is a σ-ample line bundle. We conjecture that if X admits a wild automorphism then every irreducible component of X is an abelian variety. We prove several results in support of this conjecture; in particular, we show that the conjecture is true if dimX ≤ 2. In the case where X is an abelian variety, we describe all wild automorphisms of X. Finally, we show that if A is projectively simple and admits a balanced dualizing complex, then projA is Cohen-Macaulay and Gorenstein.
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تاریخ انتشار 2005