Normal split divisors in rational homogeneous spaces

TL;DR

This paper proves that divisors with split normal sequences in rational homogeneous varieties are essentially preimages of hyperplane sections in projective spaces or quadrics, revealing a structural characterization.

Contribution

It establishes a classification of such divisors, linking their structure to hyperplane sections in classical varieties, which was previously unknown.

Findings

Divisors with split normal sequences correspond to hyperplane sections.

The result applies to rational homogeneous varieties.

Provides a structural characterization of these divisors.

Abstract

We show that a divisor in a rational homogenous variety with split normal sequence is the preimage of a hyperplane section in either the projective space or a quadric.