论文标题
共同体跳跃基因座和绝对套件的单数品种
Cohomology jump loci and absolute sets for singular varieties
论文作者
论文摘要
我们将平滑代数品种的Betti模量空间的绝对子集扩展到正常品种的情况。结果，我们证明，扭曲的同种学跳跃基因座在正常品种中排名第一是翻译的siptori的有限结合。我们表明，在基础品种$ x $的情况下，与$ h^1（x，x，\ mathbb {q}）$ pure of Weighter One投影相同，在统一品种$ x $的情况下，统一的本地系统扭曲了跳跃基因座。最后，我们研究了这些基因座与Hodge理论数据的相互作用自然与平滑投射品种基本组的代表种类相关。
We extend the notion of absolute subsets of Betti moduli spaces of smooth algebraic varieties to the case of normal varieties. As a consequence we prove that twisted cohomology jump loci in rank one over a normal variety are a finite union of translated subtori. We show that the same holds for jump loci twisted by a unitary local system in the case where the underlying variety $X$ is projective with $H^1(X,\mathbb{Q})$ pure of weight one. Lastly, we study the interaction of these loci with Hodge theoretic data naturally associated to the representation variety of fundamental groups of smooth projective varieties.
