On K\"uchle manifolds with Picard number greater than 1

TL;DR

This paper explores the geometric properties and derived categories of K"uchle varieties, a class of Fano 4-folds with higher Picard numbers, expanding understanding of their structure within algebraic geometry.

Contribution

It provides a detailed description of K"uchle varieties with Picard number greater than 1 and analyzes their derived categories, a novel contribution to the study of these Fano 4-folds.

Findings

Characterization of K"uchle varieties with Picard number > 1

Structure analysis of their derived categories

Insights into their geometric properties

Abstract

We describe the geometry of K\"uchle varieties (i.e. Fano 4-folds of index 1 contained in the Grassmannians as zero loci of equivariant vector bundles) with Picard number greater than 1 and the structure of their derived categories.