A birational involution
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911158394421248 |
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| author | Beri, Pietro Manivel, Laurent |
| author_facet | Beri, Pietro Manivel, Laurent |
| contents | 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 $G_2(R)$ 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. We deduce that $ϕ$ is an instance of a Mukai flop. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_12866 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A birational involution Beri, Pietro Manivel, Laurent Algebraic Geometry 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 $G_2(R)$ 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. We deduce that $ϕ$ is an instance of a Mukai flop. |
| title | A birational involution |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2211.12866 |