Séminaires : Séminaire de géométrie algébrique

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Le jeudi à 14h.
septembre-décembre ENS, janvier-mars Jussieu, avril-juin Sophie-Germain

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Orateur(s) Tommaso de Fernex - ,
Titre Grothendieck–Lefschetz theorem for smooth ample subvarieties and a conjecture of Sommese
Horaire17:00 à 18:00

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The notion of ample subscheme can be traced back to the work of Hartshorne and was recently formalized by Ottem. In this talk, I will discuss an extension of the Grothendieck-Lefschetz theorem to ample subvarieties and some applications to abelian varieties. I will then address a conjecture of Sommese on the extension of fiber structures from an ample subvariety to its ambient variety. Using cohomological methods, I will outline a solution of the conjecture which relies on strengthening the positivity assumption in a suitable arithmetic sense; the same methods can be applied to verify the conjecture in special cases. A different approach based on deformation theory of rational curves leads to a proof of the conjecture for smooth fibrations with rationally connected fibers and a classification theorem for projective bundles and quadric fibrations. The talk is based on joint work with Chung Ching Lau.