Fano fourfolds of K3 type

Marcello Bernardara (1) , Enrico Fatighenti (2) , Laurent Manivel (1) , Fabio Tanturri (3)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
3 UniGe - Università degli studi di Genova = University of Genoa

We produce a list of 64 families of Fano fourfolds of K3 type, extracted from our database of at least 634 Fano fourfolds constructed as zero loci of general global sections of completely reducible homogeneous vector bundles on products of flag manifolds. We study the geometry of these Fano fourfolds in some detail, and we find the origin of their K3 structure by relating most of them either to cubic fourfolds, Gushel-Mukai fourfolds, or actual K3 surfaces. Their main invariants and some information on their rationality and on possible semiorthogonal decompositions for their derived categories are provided.

Domaines: Géométrie algébrique [math.AG]

Marcello Bernardara, Enrico Fatighenti, Laurent Manivel, Fabio Tanturri. Fano fourfolds of K3 type. 2022. ⟨hal-03514383⟩