# Séminaires : Séminaire de géométrie algébrique

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 Orateur(s) Francesco Russo - , Titre Rationality of  cubic fourfolds via Trisecant Flops and via (non minimal) associated K3 surfaces. Date 06/02/2020 Horaire 14:00 à 15:30 Diffusion Résume Résumé: According to Kuznetsov Conjecture, in the moduli space of cubic fourfolds there exist infinitely many irreducible divisors (cubics of “admissible discriminant d” in the sense of Hassett), whose union should be  the locus of rational cubic fourfolds. Via the construction of the Trisecant Flops and via the theory of the congruences of $3e-1$-secant curves of degree $e$ to surfaces in P5, we shall explain the role played by “associated" (non minimal) K3 surfaces in various rationality questions regarding cubic and Gushel-Mukai fourfolds. As an application we shall present uniform proofs of the cases d=14, 26, 38 and 42 of the Conjecture, classically known only for d=14 (Fano, 1943), and discuss further possible developments of this circle of ideas. This is joint work with Giovanni Staglianò. Salle Jussieu 15-25 502 Adresse Jussieu