The relative pluricanonical stability for 3-folds of general type期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The relative pluricanonical stability for 3-folds of general type

Authors:	Meng Chen

Institution:	Department of Applied Mathematics, Tongji University, Shanghai, 200092, People's Republic of China

Abstract:	The aim of this paper is to improve a theorem of János Kollár by a different method. For a given smooth complex projective threefold of general type, suppose the plurigenus $P_{k}(X)\ge 2$ . Kollár proved that the -canonical map is birational. Here we show that either the -canonical map or the -canonical map is birational and that the -canonical map is stably birational onto its image. Suppose $P_{k}(X)\ge 3$ . Then the -canonical map is birational for $m\ge 10k+8$ . In particular, $\phi_{12}$ is birational whenever $p_{g}(X)\ge 2$ and $\phi_{11}$ is birational whenever $p_{g}(X)\ge 3$ .

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