Ueda theory for compact curves with nodes

2015/07/01 by Takayuki Koike, Koike, Takayuki · 1 citation
Mathematics · #14C20 #32J25 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1507.00109

openalex publication_date 2015/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a compact complex curve included in a non-singular complex surface such that the normal bundle is topologically trivial. Ueda studied complex analytic properties of a neighborhood of C when C is non-singular or is a rational curve with a node. We propose an analogue of Ueda's theory for the case where C admits nodes. As an application, we study singular Hermitian metrics with semi-positive curvature on the anti-canonical bundle of the blow-up of the projective plane at nine points in arbitrary position.

Citations

• On minimal singular metrics of certain class of line bundles whose section ring is not finitely generated

Cited by

• Pluripotential geometry on semi-positive effective divisors of numerical dimension one

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