Abstract
We characterize a certain neck-pinching degeneration of (marked) CP1 -structures on a closed oriented surface S of genus at least two. In a more general setting, we take a path of CP1 -structures Ct (t ⩾ 0) on S that leaves every compact subset in its deformation space, such that the holonomy of Ct converges in the PSL2C -character variety as t → ∞ . Then, it is well known that the complex structure Xt of Ct also leaves every compact subset in the Teichmüller space of S . In this paper, under an additional assumption that Xt is pinched along a loop m on S , we describe the limit of Ct from different perspectives: namely, in terms of the developing maps, holomorphic quadratic differentials, and pleated surfaces. The holonomy representations of CP1 -structures on S are known to be nonelementary (i.e., strongly irreducible and unbounded). We also give a rather exotic example of such a path Ct whose limit holonomy is the trivial representation.