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Article Dans Une Revue Science in China Series A: Mathematics Année : 2011

On nodal prime Fano threefolds of degree 10

Résumé

We study the geometry and the period map of nodal complex prime Fano threefolds with index 1 and degree 10. We show that these threefolds are birationally isomorphic to Verra solids (hypersurfaces of bidegree $(2,2)$ in $ \P^2\times \P^2$). Using Verra's results on the period map for these solids and on the Prym map for double étale covers of plane sextic curves, we prove that the fiber of the period map for our nodal threefolds is birationally the union of two surfaces, for which we give several descriptions. This result is the analog in the nodal case of a result obtained in arXiv:0812.3670 for the smooth case.
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hal-00476513 , version 1 (26-04-2010)

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Olivier Debarre, Atanas Iliev, Laurent Manivel. On nodal prime Fano threefolds of degree 10. Science in China Series A: Mathematics, 2011, 54, pp.1591-1609. ⟨hal-00476513⟩
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