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arXiv · 1910.10533

Double Veronese cones with 28 nodes

Hamid Abban·Ivan Cheltsov·Jihun Park·Constantin Shramov
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Abstract

We study nodal del Pezzo 3-folds of degree $1$ (also known as double Veronese cones) with $28$ singularities, which is the maximal possible number of singularities for such varieties. We show that they are in one-to-one correspondence with smooth plane quartics and use this correspondence to study their automorphism groups. As an application, we find all $G$-birationally rigid varieties of this kind, and construct an infinite number of non-conjugate embeddings of the group $\mathfrak{S}_4$ into the space Cremona group.

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Hamid Abban, Ivan Cheltsov, Jihun Park, Constantin Shramov. 2019-11-05. Double Veronese cones with 28 nodes. https://arxiv.org/abs/1910.10533

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