Stability of homogeneous vector bundles on \({\mathbb{C}}{\mathbb{P}}_ n\)
The author gives a criterion for the stability of homogeneous vector bundles on \({\mathbb{C}}{\mathbb{P}}_ n\). He shows that the stability of algebraic homogeneous vector bundles on \({\mathbb{C}}{\mathbb{P}}_ n\) can be described in terms of homogeneous subbundles. The basic point for this description is the construction of a unique semistable homogeneous subbundle F for every nonstable homogeneous vector bundle E such that \(\mu (F)>\mu (E)\). Here, \(\mu (E):=\) Chern class of E/rank of E, which we call the slope of E. This means that the existence of F contradicts the stability of E. Therefore, we obtain the following criterion: An algebraic homogeneous vector bundle E on \({\mathbb{C}}{\mathbb{P}}_ n\) is stable if and only if for all homogeneous subbundles F of E with \(0<\text{rank}(F)<text{rank}(E)\) we have \(\mu (F)>\mu (E)\).
stability of algebraic homogeneous vector bundles
scientific article; zbMATH DE number 4214188