论文标题
berndtsson-lempert-szőke田间与矢量束的适当全态家族相关的领域
Berndtsson-Lempert-Szőke Fields Associated to Proper Holomorphic Families of Vector Bundles
论文作者
论文摘要
Drawing on work of Berndtsson and of Lempert and Szőke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but nevertheless have a reasonable definition of curvature that agrees with the curvature of the Chern connection when the family of Hilbert spaces is locally trivial.因此，我们获得了著名的伯恩茨森定理的新证明，内容涉及半旋转扭曲的相对规范束的直接图像（即，伴随捆绑包）及其由于刘和杨而引起的更高概括。
Drawing on work of Berndtsson and of Lempert and Szőke, we define a kind of complex analytic structure for families of (possibly finite-dimensional) Hilbert spaces that might not fit together to form a holomorphic vector bundle but nevertheless have a reasonable definition of curvature that agrees with the curvature of the Chern connection when the family of Hilbert spaces is locally trivial. We thus obtain a new proof of a celebrated theorem of Berndtsson on the curvature of direct images of semi-positively twisted relative canonical bundles (i.e., adjoint bundles), and of its higher-rank generalization due to Liu and Yang.
