关于LeBrun扭量空间的多重半反正则系
On pluri-half-anticanonical system of LeBrun twistor spaces
摘要：
本文研究了LeBrun扭量空间上的多重半反正则系统。我们确定它的尺寸，基地轨迹，结构的相关的合理的地图，也结构的一般成员，在精确的形式。特别地，我们证明了当n>2和m>1时，系统的基轨迹|mK^{-1/2}|由两条非奇异的有理曲线组成，沿着这两条曲线的任何成员都具有奇异性，如果我们将这些曲线爆破，则|mK^{-1/2}|成为不可约的非奇异曲面。当n>3，m>n-2时，最后一个曲面是一般类型的无规极小曲面.我们还证明了与系统相关联的有理映射|mK^{-1/2}|是双有理的当且仅当m> n-2。
英文摘要：
In this note, we investigate pluri-half-anticanonical systems on the so called LeBrun twistor spaces. We determine its dimension, the base locus, structure of the associated rational map, and also structure of general members, in precise form. In particular, we show that if n>2 and m>1, the base locus of the system |mK^{-1/2}| on nCP^2 consists of two non-singular rational curves, along which any member has singularity, and that if we blow-up these curves, then the strict transform of a general members of |mK^{-1/2}| becomes an irreducible non-singular surface. We also show that if n>3 and m>n-2, then the last surface is a minimal surface of general type with vanishing irregularity. We also show that the rational map associated to the system |mK^{-1/2}| is birational if and only if m> n-2.
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