Neck-pinching of -structures in the -character variety.

We characterize a certain neck-pinching degeneration of (marked) -structures on a closed oriented surface of genus at least two. In a more general setting, we take a path of -structures on that leaves every compact subset in its deformation space, such that the holonomy of converges in the -character variety as . Then, it is well known that the complex structure of also leaves every compact subset in the Teichmüller space of . In this paper, under an additional assumption that is pinched along a loop on , we describe the limit of from different perspectives: namely, in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. The holonomy representations of -structures on are known to be nonelementary (i.e., strongly irreducible and unbounded). We also give a rather exotic example of such a path whose limit holonomy is the trivial representation.