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arXiv · 2501.05352

Monge-Amp\`ere type equation for the Nakano positive curvature tensor of holomorphic vector bundles

Changpeng Pan
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Abstract

For any Hermitian holomorphic vector bundle with Nakano positive curvature tensor, Demailly introduced a Monge-Amp\`ere type equation. When the rank of the bundle is $1$, it becomes the usual Monge-Amp\`ere equation. In this paper, we solve this equation in the conformal class of a Nakano positive Hermitian metric.

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Changpeng Pan. 2025-01-09. Monge-Amp\`ere type equation for the Nakano positive curvature tensor of holomorphic vector bundles. https://arxiv.org/abs/2501.05352

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