Double Veronese cones with 28 nodes

  • Hamid Abban

    University of Nottingham, Nottingham, UK
  • Ivan Cheltsov

    The University of Edinburgh, Edinburgh, UK; National Research University Higher School of Economics, Moscow, Russia
  • Jihun Park

    Institute for Basic Science, Gyeongbuk, Korea; Pohang University of Science and Technology, Gyeongbuk, Korea
  • Constantin Shramov

    Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia; National Research University Higher School of Economics, Moscow, Russia
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Abstract

We study nodal del Pezzo -folds of degree (also known as double Veronese cones) with  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 -birationally rigid varieties of this kind, and construct an infinite number of non-conjugate embeddings of the group into the space Cremona group.

Cite this article

Hamid Abban, Ivan Cheltsov, Jihun Park, Constantin Shramov, Double Veronese cones with 28 nodes. Enseign. Math. (2024), published online first

DOI 10.4171/LEM/1067