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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Zariski's theorem on several linear systems

Author: Arthur Ogus
Journal: Proc. Amer. Math. Soc. 37 (1973), 59-62
MSC: Primary 14C20
MathSciNet review: 0313259
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Abstract: We give a modern and fairly easy proof of (a slight improvement of) an important theorem of Zariski. The result gives conditions under which certain multigraded rings and modules associated with n linear systems are finitely generated, in a very strong sense.

References [Enhancements On Off] (What's this?)

  • [1] Oscar Zariski, The theorem of Riemann-Roch for high multiples of an effective divisor on an algebraic surface, Ann. of Math. (2) 76 (1962), 560–615. MR 0141668
  • [2] Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 0068874
  • [3] W. V. D. Hodge and D. Pedoe, Methods of algebraic geometry. Vol. 2, Cambridge Univ. Press, New York, 1968.

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Keywords: Linear system, base point, cohomology
Article copyright: © Copyright 1973 American Mathematical Society