论文标题
在表面的固定部分
On the fixed part of pluricanonical systems for surfaces
论文作者
论文摘要
我们表明$ | mk_x | $定义了一张男性地图，并且对于任何$ \ frac {1} {2} {2} $ -lc-lc surface $ x $，对于某些有限的正整数$ m $没有固定零件。对于每个正整数$ n \ geq 3 $，我们构造一系列投影表面$ x_ {n，i} $，使得$ k_ {x_ {x_ {n，i}} $很丰富，$ {\ rm {\ rm {mld}}} $ \ lim_ {i \ rightarrow+\ infty} {\ rm {mld}}（x__ {n，i}）= \ frac {1} {n} $，对于任何积极的整数$ m $，都存在$ i $ i $ i $ y $ y $ y $ | | mk_ {x_ {x__ {x _ {n，i}}} nonne} nonnem} nonne}}}}}}}}}。这些结果回答了XU问题的表面情况。
We show that $|mK_X|$ defines a birational map and has no fixed part for some bounded positive integer $m$ for any $\frac{1}{2}$-lc surface $X$ such that $K_X$ is big and nef. For every positive integer $n\geq 3$, we construct a sequence of projective surfaces $X_{n,i}$, such that $K_{X_{n,i}}$ is ample, ${\rm{mld}}(X_{n,i})>\frac{1}{n}$ for every $i$, $\lim_{i\rightarrow+\infty}{\rm{mld}}(X_{n,i})=\frac{1}{n}$, and for any positive integer $m$, there exists $i$ such that $|mK_{X_{n,i}}|$ has non-zero fixed part. These results answer the surface case of a question of Xu.
