On the global structure of special cycles on unitary Shimura varieties

Abstract

In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for GU(1; n-1). We explicitly compute the global structure of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, in terms of Bruhat-Tits theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport.