Berndtsson-Lempert-Sz\H{o}ke Fields Associated to Proper Holomorphic Families of Vector Bundles

Autor:	Varolin, Dror
Rok vydání:	2022
Předmět:	Mathematics - Complex Variables Mathematics - Algebraic Geometry Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	Drawing on work of Berndtsson and of Lempert and Sz\H{o}ke, 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. Comment: 64 pages. Final Version. To appear in Advances in Math
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.12802 Zobrazit plný text záznamu View this record from Arxiv