2024/03/07 by Papazachariou, Thedoros S. · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2403.04544
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.