Fano 3-folds from homogeneous vector bundles over Grassmannians

TL;DR

This paper reclassifies Fano 3-folds by representing each family as zero loci of sections of homogeneous vector bundles over Grassmannians, providing a new geometric perspective.

Contribution

It offers a unified geometric construction of all Fano 3-fold families using homogeneous vector bundles over Grassmannians, refining the Mori-Mukai classification.

Findings

Each of the 105 Fano 3-fold families is described via biregular models.

Provides explicit geometric descriptions using vector bundles over Grassmannians.

Enhances understanding of Fano 3-folds through homogeneous bundle constructions.

Abstract

We rework the Mori-Mukai classification of Fano 3-folds, by describing each of the 105 families via biregular models as zero loci of general global sections of homogeneous vector bundles over products of Grassmannians.