Weighted four-dimensional Fano hypersurfaces of K3 type

Abstract

We study weighted Fano fourfolds of K3 type realized as hypersurfaces in weighted projective spaces. Under the additional assumption that the singular locus has dimension at most one, we prove that only finitely many such families exist. We provide the complete list and analyze their rationality properties, as well as their singularities.

31 pages, 3 tables. Comments are welcome!