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• W2029121042 startingPage "365" @default.
• W2029121042 abstract "An infinite-dimensional N-graded k-algebra A is called projectively simple if dimkA/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." @default.
• W2029121042 created "2016-06-24" @default.
• W2029121042 creator A5000721810 @default.
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• W2029121042 creator A5072120928 @default.
• W2029121042 date "2006-07-01" @default.
• W2029121042 modified "2023-09-30" @default.
• W2029121042 title "Projectively simple rings" @default.
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• W2029121042 doi "https://doi.org/10.1016/j.aim.2005.04.013" @default.
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