The moduli space of genus $8$ Fano $3$-folds with two $\frac12(1,1,1)$-points: rationality and K-stability

Joseph Malbon; Alex Massarenti; Francesco Zucconi

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arXiv · 2408.13080

The moduli space of genus $8$ Fano $3$-folds with two $\frac12(1,1,1)$-points: rationality and K-stability

Joseph Malbon·Alex Massarenti·Francesco Zucconi

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Abstract

Let $\mathcal F_{8,2\times\frac12(1,1,1)}$ be the moduli space of genus $8$ Fano $3$-folds with two terminal quotient singularities of type $\frac12(1,1,1)$. We prove that $\mathcal F_{8,2\times\frac12(1,1,1)}$ is rational. Moreover, we show that a general member of this family is K-stable.

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Joseph Malbon, Alex Massarenti, Francesco Zucconi. 2024-08-23. The moduli space of genus $8$ Fano $3$-folds with two $\frac12(1,1,1)$-points: rationality and K-stability. https://arxiv.org/abs/2408.13080

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