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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.
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Preprints, Working Papers, ...
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https://hal-cnrs.archives-ouvertes.fr/hal-03860819
Contributor : Laurent Manivel Connect in order to contact the contributor
Submitted on : Monday, November 21, 2022 - 5:57:16 PM
Last modification on : Tuesday, November 22, 2022 - 4:00:20 AM

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  • HAL Id : hal-03860819, version 1
  • ARXIV : 2211.12866

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

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