A GENERALIZATION OF PRINCIPAL BUNDLES WITH A PARABOLIC OR LEVEL STRUCTURE

We define a parameter-dependent notion of stability for principal bundles with a certain local decoration, which generalizes both parabolic and level structures, and construct their coarse moduli space. A necessary technical step is the construction of the moduli space of tuples of vector bundles with a global and a local decoration, which we call locally decorated tumps. We introduce a notion of asymptotic stability for locally decorated tumps and show that stable locally decorated principal bundles can be described as asymptotically stable locally decorated tumps.