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

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.