关于复曲面基本群的正规子群
On normal subgroups in the fundamental groups of complex surfaces
摘要：
我们证明了，对于每个非球面紧致复曲面$X$，如果其基本群$π$满足短正合序列$$ 1\to K \to π\to π_1(S) \to 1 $$，其中$S$是紧致双曲Riemann曲面，且$K$是有限可表示的，则存在$S$上的复结构和诱导上述短正合序列的非奇异全纯纤维化$f: X\to S$.特别地，紧致复双曲曲面的基本群不能满足上述短正合列。作为应用，我们给出了$PU(2,1)$中非相干均匀晶格的第一个例子。
英文摘要：
We show that for each aspherical compact complex surface $X$ whose fundamental group $π$ fits into a short exact sequence $$ 1\to K \to π\to π_1(S) \to 1 $$ where $S$ is a compact hyperbolic Riemann surface and the group $K$ is finitely-presentable, there is a complex structure on $S$ and a nonsingular holomorphic fibration $f: X\to S$ which induces the above short exact sequence. In particular, the fundamental groups of compact complex-hyperbolic surfaces cannot fit into the above short exact sequence. As an application we give the first example of a non-coherent uniform lattice in $PU(2,1)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
