中国科大学位与研究生教育
课程名称: 教师:
当前位置:
 >> 
 >> 
Topology of subvarieties of complex semi-abelian varieties
Topology of subvarieties of complex semi-abelian varieties
教师介绍

本讲教师:Yongqiang Liu
所属学科:理科
人  气:567

课程介绍
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.

评论

针对该课程没有任何评论,谈谈您对该课程的看法吧?
  • 用户名: 密 码:
致谢:本课件的制作和发布均为公益目的,免费提供给公众学习和研究。对于本课件制作传播过程中可能涉及的作品或作品部分内容的著作权人以及相关权利人谨致谢意!
课件总访问人次:11432395
中国科学技术大学研究生网络课堂试运行版,版权属于中国科学技术大学研究生院。
本网站所有内容属于中国科学技术大学,未经允许不得下载传播。
地址:安徽省合肥市金寨路96号;邮编:230026。TEL:+86-551-63602922;E-mail:wlkt@ustc.edu.cn。