标题： Tannaka群$E_6$仅来自三次三维立体 显示英文标题

标题： The Tannaka group $E_6$ only arises from cubic threefolds

摘要： 我们证明，在温和的假设下，光滑三次三维流形上的Fano曲线面是阿贝尔簇中唯一的光滑子概形，其 perverse 混合层卷积的Tannaka群是一个例外简单群。 这特别导致了我们之前在Shafarevich猜想方面的研究的重大加强。 一个关键思想是通过Hodge模的Tannaka群的一个共轭来控制上同调上的Hodge分解，并将其与Lazarsfeld-Popa和Lombardi对不规则概形的Hodge数估计的改进进行对比。 显示英文摘要

摘要： We show that under mild assumptions, the Fano surfaces of lines on smooth cubic threefolds are the only smooth subvarieties of abelian varieties whose Tannaka group for the convolution of perverse sheaves is an exceptional simple group. This in particular leads to a considerable strengthening of our previous work on the Shafarevich conjecture. A key idea is to control the Hodge decomposition on cohomology by a cocharacter of the Tannaka group of Hodge modules, and to play this off against an improvement of the Hodge number estimates for irregular varieties by Lazarsfeld-Popa and Lombardi.