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arXiv · 2403.04544

On products of K-moduli spaces

Thedoros S. Papazachariou
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Abstract

We study the K-moduli space of products of Fano varieties in relation to the product of K-moduli spaces of the product components. We show that there exists a well-defined morphism from the product of K-moduli stacks of Fano varieties to the K-moduli stack of their product. Furthermore, we show that this morphism is an isomorphism if any two varieties with different irreducible components are non-isomorphic, and a torsor if they are. Our results rely on the theory of stacks and previous work by Zhuang. We use our main result to obtain an explicit description of the K-moduli stack/ space of Fano threefolds with Picard rank greater than 6, along with a wall-crossing description, and a detailed polyhedral wall-crossing description for K-moduli of log Fano pairs.

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Thedoros S. Papazachariou. 2024-03-07. On products of K-moduli spaces. https://arxiv.org/abs/2403.04544

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