论文标题
非理性铅笔和贝蒂数字
Irrational pencils and Betti numbers
论文作者
论文摘要
我们研究了紧凑的非球形复合歧管上具有孤立临界点的非理性铅笔。我们证明，如果临界点是非空的，那么铅笔在基本群体上引起的形态的核的同源性就不会有限地产生。这概括了Dimca，Papadima和Suciu的结果。通过考虑Cartwright-Steger表面的自我产生，这使我们能够构建新的光滑投射品种的例子，其基本组具有非最初产生的同源性。
We study irrational pencils with isolated critical points on compact aspherical complex manifolds. We prove that if the set of critical points is nonempty, the homology of the kernel of the morphism induced by the pencil on fundamental groups is not finitely generated. This generalizes a result by Dimca, Papadima and Suciu. By considering self-products of the Cartwright-Steger surface, this allows us to build new examples of smooth projective varieties whose fundamental group has a non-finitely generated homology.
