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Working paper

Double Veronese cones with 28 nodes

Shramov K., Cheltsov I., Park J., Ahmadinezhad H.
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 𝔖_4 into the space Cremona group.