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arXiv · 1507.00109

Ueda theory for compact curves with nodes

Takayuki Koike
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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.

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Takayuki Koike. 2015-07-01. Ueda theory for compact curves with nodes. https://arxiv.org/abs/1507.00109

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