A birational involution

2022/11/21 by Beri, Pietro, Manivel, Laurent · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.12866

Abstract

Given a general K3 surface S of degree 18, lattice theoretic considerations allow to predict the existence of an anti-symplectic birational involution ϕ of the Hilbert cube S^[3]. We describe this involution in terms of the Mukai model of S, with the help of the famous transitive action of the exceptional group G₂(R) on the six-dimensional sphere. We make a connection with Homological Projective Duality by showing that the indeterminacy locus of the involution is birational to a P²-bundle over the dual K3 surface of degree two. We deduce that ϕ is an instance of a Mukai flop.

Cited by

• Coble duality for Jacobian Kummer fourfolds

Related

• More birational involutions
• Birational geometry of the Mukai system of rank two and genus two
• On the Chow groups of certain EPW sextics
• EPW sextics and Hilbert squares of K3 surfaces
• Birational geometry of Beauville-Mukai systems III: asymptotic behavior