A Gieseker type degeneration of moduli stacks of vector bundles on curves

Abstract

We construct a new degeneration of the moduli stack of vector bundles over a smooth curve when the curve degenerates to a singular curve which is irreducible with one double point. We prove that the total space of the degeneration is smooth and its special fibre is a divisor with normal crossings. Furthermore, we give a precise description of how the normalization of the special fibre of the degeneration is related to the moduli space of vector bundles over the desingularized curve.