Classification of embedded projective manifolds swept out by rational homogeneous varieties of codimension one

TL;DR

This paper classifies smooth projective varieties embedded in projective space that are covered by rational homogeneous varieties with specific Picard number and codimension, providing a comprehensive understanding of their structure.

Contribution

It offers a complete classification of embedded projective varieties swept out by rational homogeneous varieties with Picard number and codimension equal to one.

Findings

Provides a classification of such varieties

Identifies key geometric properties of these varieties

Enhances understanding of rational homogeneous varieties in projective geometry

Abstract

We give a classification of embedded smooth projective varieties swept out by rational homogeneous varieties whose Picard number and codimension are one.