Degenerate, strong and stable Yang-Mills-Higgs pairs

In this paper, we introduce some notions on the Hitchin pair consisting of a Chern connection and a Higgs field closely related to the first and second variations of Yang-Mills-Higgs functional, such as degenerate Hitchin pair, (strong) Yang-Mills-Higgs pair, and stable Yang-Mills-Higgs pair. We investigate some properties of such pairs under the various contexts.