曲面上$\mathbb{Q}$-因子的Sakai定理及其应用

IF 0.5 4区数学 Q3 MATHEMATICS

Asian Journal of Mathematics Pub Date : 2018-08-31 DOI:10.4310/AJM.2018.V22.N4.A8

Fei Ye, Tongde Zhang, Zhixian Zhu

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引用次数: 1

摘要

本文推广了Sakai [Sak90]关于D积分的结果，给出了光滑投影曲面S上D2 > 0和H1(OS(−D)) = 0的大q因子D的刻画。作为这一结果在q -除数上的应用，我们证明了伴随线性系统|KS + D|的基点自由性和非常充裕性的结果。这些结果可以看作是对先前在Ein-Lazarsfeld [EL93]和Ma ø sek [Ma ø s99]光滑表面上的结果的改进。

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Sakai’s theorem for $\mathbb{Q}$-divisors on surfaces and applications

In this paper, we present a characterization of a big Q-divisor D on a smooth projective surface S with D2 > 0 and H1(OS(−D)) = 0, which generalizes a result of Sakai [Sak90] for D integral. As applications of this result for Q-divisors, we prove results on base-pointfreeness and very-ampleness of the adjoint linear system |KS + D|. These results can be viewed as refinements of previous results on smooth surfaces of Ein-Lazarsfeld [EL93] and Ma¸sek [Ma¸s99].

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