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arXiv · 2505.04303

Bott-Chern complexity of K\"ahler pairs

Christopher Hacon·Joaquín Moraga·José Ignacio Yáñez
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Abstract

We introduce the Bott-Chern complexity of a compact K\"ahler pair $(X,B)$. This invariant compares $\dim(X)$, $\dim H^{1,1}_{\rm BC}(X)$ and the sum of the coefficients of $B$. When $(X,B)$ is Calabi-Yau, we show that its Bott-Chern complexity is non-negative. We prove that the Bott-Chern complexity of a Calabi-Yau compact K\"ahler pair $(X,B)$ is at least three whenever $X$ is not projective. Furthermore, we show this value is optimal and is achieved by certain singular non-projective K3 surfaces.

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Christopher Hacon, Joaquín Moraga, José Ignacio Yáñez. 2025-05-07. Bott-Chern complexity of K\"ahler pairs. https://arxiv.org/abs/2505.04303

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