ar X iv : m at h / 99 12 05 1 v 2 [ m at h . A G ] 2 9 Fe b 20 00 CRITERIA FOR σ - AMPLENESS
نویسنده
چکیده
In the noncommutative geometry of Artin, Van den Bergh, and others, the twisted homogeneous coordinate ring is one of the basic constructions. Such a ring is defined by a σ-ample divisor, where σ is an automorphism of a projective scheme X. Many open questions regarding σ-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on X to be σ-ample. As a consequence, we show right and left σ-ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms σ yield a σ-ample divisor.
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تاریخ انتشار 2008