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Invariants des variations infinitésimales de structures de Hodge et géométrie des surfaces de type général

Abstract : Let X be a complex projective manifold. One can associate to X its cohomological data (for instance, its singular cohomological groups, its Hodge decomposition, etc...). When it is possible to extract enough geometric information from these data to recover X, one says that a Torelly-type theorem holds. For the infinitesimal Torelli-type problem, one is given the information encoded by the differential of the period map. These data are IV HS(X). The aim is to recover X from IV HS(X). In 1983, R. Donagi shows that if X is a generic smooth hypersurface then IV HS(X) determines X. This thesis shows a similar result for a singular quintic surface in P P 3 : the Togliatti quintic, Σ5. This quintic has 31 nodes. This is the maximal number of ordinary double-points a quintic surface in P3 canhave. We show that if X is the minimal resolution of Σ5, IV HS(X) determines the double points. These double-points are in a specialconfiguration which can be read in IV HS(X). This determines Σ5, i.e. we show a Torelli type theorem for the Togiatti quintic.
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https://tel.archives-ouvertes.fr/tel-03860603
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Submitted on : Friday, November 18, 2022 - 4:52:18 PM
Last modification on : Saturday, November 19, 2022 - 3:27:50 AM

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  • HAL Id : tel-03860603, version 1

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Axel Supersac. Invariants des variations infinitésimales de structures de Hodge et géométrie des surfaces de type général. Géométrie algébrique [math.AG]. Université d'Angers, 2021. Français. ⟨NNT : 2021ANGE0037⟩. ⟨tel-03860603⟩

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