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Le jeudi à 14h.
|Tommaso de Fernex - ,
|Grothendieck–Lefschetz theorem for smooth ample subvarieties and a conjecture of Sommese
|17:00 à 18:00
Same access code. Send a mail to O. Debarre or F. Han or A. Höring to get it.
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.