Geodesic
Criteria for 𝜎-ampleness
Keeler, Dennis1
1 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109
Journal of the American Mathematical Society, Tome 13 (2000) no. 3, pp. 517-532 Cet article a éte moissonné depuis la source American Mathematical Society

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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 $\sigma$-ample divisor, where $\sigma$ is an automorphism of a projective scheme $X$. Many open questions regarding $\sigma$-ample divisors have remained. We derive a relatively simple necessary and sufficient condition for a divisor on $X$ to be $\sigma$-ample. As a consequence, we show right and left $\sigma$-ampleness are equivalent and any associated noncommutative homogeneous coordinate ring must be noetherian and have finite, integral GK-dimension. We also characterize which automorphisms $\sigma$ yield a $\sigma$-ample divisor.
DOI : 10.1090/S0894-0347-00-00334-9

Keeler, Dennis 1

1 Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1109 
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Keeler, Dennis. Criteria for 𝜎-ampleness. Journal of the American Mathematical Society, Tome 13 (2000) no. 3, pp. 517-532. doi: 10.1090/S0894-0347-00-00334-9

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