Ample filters of invertible sheaves |
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Institution: | Department of Mathematics, MIT, Cambridge, MA 02139-4307, USA |
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Abstract: | Let X be a scheme, proper over a commutative Noetherian ring A. We introduce the concept of an ample filter of invertible sheaves on X and generalize the most important equivalent criteria for ampleness of an invertible sheaf. We also prove the Theorem of the Base for X and generalize Serre's Vanishing Theorem. We then generalize results for twisted homogeneous coordinate rings which were previously known only when X was projective over an algebraically closed field. Specifically, we show that the concepts of left and right σ-ampleness are equivalent and that the associated twisted homogeneous coordinate ring must be Noetherian. |
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