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arXiv · 2211.10925

Blow-ups and modifications of lcK spaces

Ovidiu Preda·Miron Stanciu
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Abstract

In this article, we prove that the blow-up of a locally irreducible lcK space $X$ along a subspace $Z$ which verifies certain conditions is lcK if and only if $X$ is induced gcK, generalizing a theorem of Ornea-Verbitsky-Vuletescu to singular locally irreducible spaces. We also show that even if modifications of lcK spaces are not always of lcK type, they always admit quasi-lcK metrics.

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Ovidiu Preda, Miron Stanciu. 2022-11-20. Blow-ups and modifications of lcK spaces. https://arxiv.org/abs/2211.10925

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