A Gieseker type degeneration of moduli stacks of vector bundles on   curves
  Given a generically smooth stable curve over a discrete valuation ring such that its special fibre is irreducible with one double point, we construct a moduli stack over that descrete valuation ring which is a model for the moduli stack of vector bundles over the generic fibre of the curve. The model has the following nice properties:   1. It is regular.   2. Its special fibre is a normal crossing divisor.   3. The normalization of its special fibre is a locally trivial KGl-bundle over the moduli stack of vector bundles over the normalization of the special fibre of the curve.   Here KGl is a canonical compactification of the general linear group. Our motivation is that such a model may help to give recursion formulae for such cohomological invariants of the moduli stack of vector bundles on smooth curves which depend only on the genus of the curve. 
Ivan Kausz