Abstract:We introduce a generalized first Ueda obstruction class for a line bundle along a closed analytic subvariety of a complex manifold, allowing singular subvarieties and restrictions that are not unitary flat. Using a Dolbeault resolution, the Chern curvature appears naturally, and non-vanishing of the class obstructs the existence of a smooth Hermitian metric with semi-positive curvature. As an application, we recover several classical examples within a unified framework and provide new examples of nef but not semi-positive line bundles. We also introduce higher degree analogues of these obstruction classes.
From: Xiaojun Wu [view email]
[v1]
Mon, 22 Jun 2026 03:54:51 UTC (28 KB)
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