$$L^2$$-extension of adjoint bundles and Kollár’s conjecture
$$L^2$$-extension of adjoint bundles and Kollár’s conjecture
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$$L^2$$-伴随丛的扩展和Kollárâs猜想
DOI：
10.1007/s00208-022-02432-6
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发表时间：
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影响因子：
1.4
通讯作者：
Chen Zhao
中科院分区：
文献类型：
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作者：
Junchao Shentu;Chen Zhao
我们给出了Kollár关于霍奇结构的一种变异扭曲的对偶化束的导出推力的猜想的一个新的证明。这一猜想已经由Saito先生通过混合Hodge模块理论解决，并在Albanese地图的研究中有各种应用。我们的技术是（L^2）理论，它给出了猜想的具体构造和证明。（L^2）的观点允许我们将Kollár的猜想推广到非阿贝尔霍奇理论的背景下。
We give a new proof of Kollár’s conjecture on the derived pushforward of the dualizing sheaf twisted by a variation of Hodge structure. This conjecture has been settled by M. Saito via the theory of mixed Hodge modules and has various applications in the investigation of Albanese maps. Our technique is (L^2) theoretic which gives concrete constructions and proofs to the conjecture. The (L^2) point of view allows us to generalize Kollár’s conjecture to the context of non-abelian Hodge theory.