On the geometry of some quiver zero loci Fano fourfolds (with an appendix by E. Kalashnikov and F. Tufo)

TL;DR

This paper classifies and describes 170 families of Fano fourfolds arising as quiver flag zero loci, providing geometric interpretations and detailed birational and biregular analyses.

Contribution

It offers a comprehensive classification and geometric understanding of 170 families of quiver flag zero loci Fano fourfolds, expanding the knowledge of their structure and properties.

Findings

170 families of Fano fourfolds classified

Birational and biregular descriptions provided

Geometric interpretations as zero loci of sections of vector bundles

Abstract

In this paper, we study 170 families of quiver flag zero loci Fano fourfolds as described by Kalashnikov. We interpret those manifolds as zero loci of sections of homogeneous vector bundles in homogeneous varieties, and we give a birational and biregular description of all 170 families.