Effective behavior of multiple linear systems
Algebraic Geometry
2007-05-23 v1
Abstract
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.
Cite
@article{arxiv.math/0312078,
title = {Effective behavior of multiple linear systems},
author = {Sheng-Li Tan},
journal= {arXiv preprint arXiv:math/0312078},
year = {2007}
}
Comments
Latex, 17 pages. Asian Journal of Mathematics (to appear)