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

Voir la notice de l'article provenant de la source American Mathematical Society

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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