On Moduli Description of Local Models For Ramified Unitary Groups and Resolution of Singularity

Local models are schemes which are intended to model the \'etale-local structure of $p$-adic integral models of Shimura varieties. In the setting of local models for ramified unitary groups, Smithling has proposed a further refinement to the moduli problems in Pappas and Rapoport's work to characterize the local model. In this paper we examine a special case with signature $(n-1,1)$ under this construction, and propose a moduli description for resolution of singularities