Effective behavior of multiple linear systems

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We give optimal effective bounds for some well-known theorems on complex algebraic surfaces, which are respectively due to Serre, Zariski (1962), Castelnuovo (1897), Artin (1962, 1966), Benveniste (1984), Cutkosky and Srinivas (1993). These theorems are about Riemann-Roch problem (on the behavior of the function dim |nD| of n), vanishing theorems, base-point freeness and k-very ampleness of the linear systems |nD| and |nA+L|, where D is effective, A is nef and big and L is arbitrary. As a consequence, we obtain an effective version of Matsusaka's big theorem, and we give also examples to show that our bound is the best possible one.
Latex, 17 pages. Asian Journal of Mathematics (to appear)

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Algebraic Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/69449

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0312078
 http://arxiv.org/abs/math/0312078

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arXiv