Title: High-pliability Fano hypersurfaces Show Chinese title

Title: 高可塑性法诺超曲面

Abstract: We show that five of Reid's Fano 3-fold hyperurfaces containing at least one compound Du Val singularity of type $cA_n$ have pliability at least two. The two elements of the pliability set are the singular hypersurface itself, and another non-isomorphic Fano hypersurface of the same degree, embedded in the same weighted projective space, but with different compound Du Val singularities. The birational map between them is the composition of two birational links initiated by blowing up two Type I centres on a codimension 4 Fano 3-fold of $\mathbb{P}^2 \times \mathbb{P}^2$-type having Picard rank 2. Show Chinese abstract

Abstract: 我们证明了包含至少一个类型为$cA_n$的复合 Du Val 奇点的五个 Reid 的 Fano 3-维超曲面具有至少两个的可塑性。 可塑性集的两个元素是该奇异超曲面本身，以及另一个不同构的同次数的 Fano 超曲面，它嵌入在相同的加权射影空间中，但具有不同的复合 Du Val 奇点。 它们之间的有理映射是由在具有 Picard 秩 2 的 4-余维的$\mathbb{P}^2 \times \mathbb{P}^2$类 Fano 3-维流形上对两个 I 型中心进行爆破所引发的两个有理链的复合。