论文标题
关于表面上的补充的评论
Remark on complements on surfaces
论文作者
论文摘要
我们对任何维度的特殊对的奇异对奇异性进行了明确的表征。特别是，我们表明任何异常的Fano Surface都是$ \ frac {1} {42} $ -LC。作为冠冕，我们表明任何$ \ mathbb r $ - complementary $ x $对于某些整数$ n \ leq 192 \ cdot 84^{128 \ cdot 42^5} \ 10 3 \ sqrt {2} \ cdot 84^{64 \ cdot 42^5} \ about 10^{10^{10.2}} $。尽管后两个值预计远非最佳，但它们是这两个代数不变的表面上的第一个明确上限。
We give an explicit characterization on the singularities of exceptional pairs in any dimension. In particular, we show that any exceptional Fano surface is $\frac{1}{42}$-lc. As corollaries, we show that any $\mathbb R$-complementary surface $X$ has an $n$-complement for some integer $n\leq 192\cdot 84^{128\cdot 42^5}\approx 10^{10^{10.5}}$, and Tian's alpha invariant for any surface is $\leq 3\sqrt{2}\cdot 84^{64\cdot 42^5}\approx 10^{10^{10.2}}$. Although the latter two values are expected to be far from being optimal, they are the first explicit upper bounds of these two algebraic invariants for surfaces.
