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A birational involution


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.
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hal-03860819 , version 1 (21-11-2022)



Pietro Beri, Laurent Manivel. A birational involution. 2022. ⟨hal-03860819⟩
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