AI 中文总结
本文针对具有平凡判别式的一般韦伊型阿贝尔四维流形的霍奇猜想给出新证明。借助其到\(K3^{[3]}\)型超凯勒六维流形的映射，通过超凯勒流形双有理几何及形变理论成果，得出六维流形切丛第二陈类拉回相关代数类结论。
AI 中文摘要
对于具有平凡判别式的一般韦伊型阿贝尔四维流形，目前已有多种关于霍奇猜想的证明，本文给出另一种。所考虑的阿贝尔四维流形允许有到\(K3^{[3]}\)型超凯勒六维流形的映射。六维流形切丛的第二陈类的拉回是二维余维的代数类，且不是除子类的交，由此得出主要结果。在回顾韦伊型阿贝尔四维流形的基本事实后，利用这些超凯勒流形的双有理几何结果和形变理论建立了映射的存在性。
英文摘要
There are now several proofs of the Hodge conjecture for the general abelian fourfold of Weil type with trivial discriminant. This paper provides another one. The abelian fourfolds under consideration allow a map to a hyperkähler sixfold of K3$^{[3]}$ type. The pull-back of the second Chern class of the tangent bundle of the sixfold is an algebraic class in codimension two that is not an intersection of divisor classes and the main result follows. After recalling the basic facts on abelian fourfolds of Weil type we establish the existence of the map using results on the birational geometry of these hyperkähler manifolds and deformation theory.
