A birational involution
Abstract
Given a general K3 surface S of degree 18, lattice theoretic considerations allow to predict the existence of an anti-symplectic birational involution 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 G_2(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 P^2-bundle over the dual K3 surface of degree two.
Origin : Files produced by the author(s)