This research aims to understand the relationship between divisors and hyperplane sections in rational homogeneous spaces.
Analyzed the structure of divisors in rational homogeneous varieties.
Investigated split normal sequences related to these divisors.
Explored the geometric implications in projective spaces and quadrics.
Identified that a divisor in a rational homogeneous variety with a split normal sequence corresponds to a hyperplane section.
Demonstrated the relationship between these geometric constructs in projective space and quadric varieties.
Abstract
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.