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High-pliability Fano hypersurfaces

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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.

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Funding

This work was supported by Korea Institute for Advanced Study, Grant No. MG087901. The author has no relevant financial or non-financial interests to disclose.

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  1. School of Mathematics, Korea Institute for Advanced Study (KIAS), 85 Hoegiro, Dongdaemun-gu, Seoul, 02455, Republic of Korea

    Livia Campo

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  1. Livia Campo
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Correspondence to Livia Campo.

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The author would like to thank Tiago Guerreiro for conversations and comments during the development of this work. The author is kindly supported by Korea Institute for Advanced Study, grant No. MG087901.

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Campo, L. High-pliability Fano hypersurfaces. Rend. Circ. Mat. Palermo, II. Ser 72, 3045–3060 (2023). https://doi.org/10.1007/s12215-023-00861-z

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