Weighted four-dimensional Fano hypersurfaces of K3 type

TL;DR

This paper classifies weighted Fano fourfolds of K3 type as hypersurfaces in weighted projective spaces, establishing finiteness, and analyzes their rationality and singularities.

Contribution

It provides a complete classification of such fourfolds with low-dimensional singular loci and examines their geometric properties.

Findings

Finitely many families exist under the given conditions

Complete classification list provided

Analyzed rationality and singularity properties

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.