Desmic quartic surfaces in arbitrary characteristic

2025/05/02 by Dolgachev, Igor, Kondo, Shigeyuki · 2 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.01033

Abstract

A desmic quartic surface is a birational model of the Kummer surface of the self-product of an elliptic curve. We recall the classical geometry of these surfaces and study their analogs in arbitrary characteristic. Moreover, we discuss the cubic line complex \frakG associated with the desmic tetrahedra introduced by G. Humbert. We prove that \frakG is a rational \bbQ-Fano threefold with 34 nodes and the group of projective automorphisms isomorphic to (\frakS₄× \frakS₄)\rtimes 2.

Citations

• The automorphism groups of Kummer surfaces in characteristic two and their complex analogues
• K3 surfaces of Kummer type in characteristic two
• Kummer surfaces and quadratic line complexes in characteristic two
• Kummer surfaces associated with group schemes
• Abstract configurations in algebraic geometry
• A supersingular K3 surface in characteristic 2 and the Leech lattice
• Heisenberg-invariant Kummer surfaces

Cited by

• F4 and desmic quartic surfaces
• K3 surfaces of degree six arising from desmic tetrahedra

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• K3 surfaces of degree six arising from desmic tetrahedra
• F4 and desmic quartic surfaces
• Kummer quartic surfaces, strict self-duality, and more
• Quartic K3 surfaces without nontrivial automorphisms
• Hessian quartic surfaces that are Kummer surfaces