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8-8吴文俊数学重点实验室微分几何系列报告【Yongqiang Liu】

题目: Topology of subvarieties of complex semi-abelian varieties

报告人:Yongqiang Liu (KU Leuven)

时间:8月8(周二)上930-1030

地点:五教5507

摘要: We use the non-proper Morse theory of Palais-Smale to investigate the topology of smooth closed subvarieties of complex semi-abelian varieties, and that of their infinite cyclic covers. As main applications, we obtain the finite generation (except in the middle degree) of the corresponding integral Alexander modules, as well as the signed Euler characteristic property and generic vanishing for rank-one local systems on such subvarieties. Furthermore, we give a more conceptual (topological) interpretation of the signed Euler characteristic property in terms of vanishing of Novikov homology. As a byproduct, we prove a generic vanishing result for the L2-Betti numbers of very affine manifolds. Our methods also recast Jun Huh's extension of Varchenko's conjecture to very affine manifolds, and provide a generalization of this result in the context of smooth closed subvarieties of semi-abelian varieties. This is a joint work with Laurentiu Maxim and Botong Wang.

 

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  科大主页 | 国家数学与交叉科学中心(合肥) | 中科院吴文俊数学重点实验室 |
中科院数学与系统科学研究院 | 北京国际数学研究中心 | 安徽省数学会