The local invariants of a meromorphic quadratic differential on a compact Riemann surface are the orders of zeros and poles, and the residues at the poles of even orders. The main result of this paper is that with few exceptions, every pattern of local invariants can be obtained by a quadratic differential on some Riemann surface. The exceptions are completely classified and only occur in genera zero and one. Moreover, in the case of a nonconnected stratum, we show that, with three exceptions in genus one, each configuration of invariants can be realized in each non-hyperelliptic connected component of the stratum. In the hyperelliptic components with two poles the residues at both poles coincide. These results are obtained using the flat metric induced by the differentials. We give an application by bounding the number of disjoint cylinders on a primitive quadratic differential.

Southern Pomo (Pomoan, California) displays a process of rhythmic vowel deletion (syncope) reflecting two mutually incompatible metrical structures. This phenomenon, called metrical incoherence, can be derived by an ordered sequence of independent subgrammars, that is, strata. Metrical incoherence is under-attested crosslinguistically, and the stratal models of phonology necessary to generate it have been criticised for predicting counter-typological phenomena. Nevertheless, the Southern Pomo data cannot be generated in more restrictive frameworks. This article argues that overgeneration is a necessary property of the phonological component, and that metrical incoherence is rare because it is difficult to learn. In Southern Pomo, this difficulty appears to have caused grammatical competition and restructuring: a second pattern of syncope, occurring in only a limited context, suggests that learners have reanalysed the grammar as having consistent metrical structure across the derivation. This work thus supports the proposal that diachronic change – and therefore typology – is constrained by extragrammatical factors.