Bounded Negativity and Arrangements of Lines
Bounded Negativity and Arrangements of Lines
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有界负性和线条的排列
DOI：
10.1093/imrn/rnu236
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
T. Szemberg
中科院分区：
文献类型：
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作者：
Thomas Bauer;S. Rocco;B. Harbourne;J. Huizenga;A. Lundman;Piotr Pokora;T. Szemberg
有界负性猜想预言，对于任何光滑的复曲面X，X上约化因子的自交存在一个下界。这个猜想是开放的。这也是不知道是否存在这样一个下界是不变的双有理等价类的$X$。在本说明中，我们引入了某些常数H（X），它实际上测量了X的双有理等价类中下界的方差。我们专注于有理曲面，并将$H（{\mathbb P}^2）$的值与某些线排列联系起来。我们的主要结果是定理3.3，主要的公开挑战是问题3.10。
The Bounded Negativity Conjecture predicts that for any smooth complex surface $X$ there exists a lower bound for the selfintersection of reduced divisors on $X$. This conjecture is open. It is also not known if the existence of such a lower bound is invariant in the birational equivalence class of $X$. In the present note we introduce certain constants $H(X)$ which measure in effect the variance of the lower bounds in the birational equivalence class of $X$. We focus on rational surfaces and relate the value of $H({\mathbb P}^2)$ to certain line arrangements. Our main result is Theorem 3.3 and the main open challenge is Problem 3.10.