2025/07/18 by Hiromichi Takagi, Takagi, Hiromichi
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Coding theory and cryptography
paper · pdf · doi:10.48550/arxiv.2507.13657
We consider the classification problem of prime ℚ-Fano 3-folds with at most 1/2(1,1,1)-singularities, which was initiated in [Taka2]. We construct two distinct classes of such 3-folds with genus one and six 1/2(1,1,1)-singularities, each equipped with a prescribed Sarkisov link. Our method involves constructing certain higher-dimensional ℚ-Fano varieties Σ, referred to as key varieties, by extending the Sarkisov links to higher dimensions. We prove that each such 3-fold X arises as a linear section of the corresponding key variety Σ, and conversely, any general linear section of Σ yields such an X. Various geometric properties of the key varieties Σ are also investigated and clarified.