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arXiv · 2308.12555

On positive semi-definite holomorphic sectional curvature with many zeroes

Minzi Chen·Gordon Heier
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Abstract

We establish the existence of complete K\"ahler metrics of semi-positive holomorphic sectional curvature with many zeroes in an interesting and natural geometric setting. Specifically, we use Calabi's Ansatz in the form due to Koiso-Sakane to produce such metrics on the total space of powers of the tautological line bundles over the projective line. We formulate a general conjecture regarding the compact case and use a product approach to obtain an analogous result in the non-compact case.

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Minzi Chen, Gordon Heier. 2023-08-24. On positive semi-definite holomorphic sectional curvature with many zeroes. https://arxiv.org/abs/2308.12555

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