Smooth Fano four folds in Gorenstein formats

TL;DR

This paper constructs new deformation families of smooth Fano fourfolds with explicit equations, expanding the known classes in Gorenstein formats and highlighting their smaller anti-canonical degrees.

Contribution

It introduces novel deformation families of Fano fourfolds in Gorenstein formats with explicit descriptions, enriching the classification of these manifolds.

Findings

Families have explicit equations in weighted projective spaces

Constructed families exhibit smaller anti-canonical degrees

Enhances understanding of Fano fourfolds in Gorenstein formats

Abstract

We construct some new deformation families of four-dimensional Fano manifolds of index $1$ in some known classes of Gorenstein formats. These families have explicit descriptions in terms of equations, defining their image under the anti-canonical embedding in some weighted projective space. The constructed families have relatively smaller anti-canonical degrees than most other known families of smooth Fano 4-folds.