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.
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