A.A. Klyachko discovered that an equivalence of categories can be established between toric vector bundles over a toric variety and multifiltered vector spaces subject
to a compatibility condition. This allows one to investigate a lot of properties of toric
vector bundles by combinatorics. Klyachko has demonstrated this method on complex
projective space. In this thesis, we apply his ideas to study toric bundles on Hirzebruch
surfaces. The focus is on characteristic classes and stability conditions.
Permanent URL for this record: https://lbezone.hkust.edu.hk/bib/991013100058103412