Linked Grassmannians and Local Models of Shimura Varieties: Unramified Type A
Linked Grassmannians are objects that arise in the study of algebraic curves, namely in limit linear series and Brill-Noether theory. It turns out that local models of Shimura varieties of PEL-type admit natural interpretations as Linked Grassmannians, and that this allows for richer class of conditions that we can impose on the local model moduli problem, of a much different flavor than ones in standard use (e.g. "wedge" or "spin" conditions). This allows us to give a moduli-theoretic definition of local models even in cases where the definition must be modified due to the naive moduli space not being flat. In this paper, we work out the case where the PEL Shimura variety is of type A, that is, for Shimura varieties associated with unitary groups.
Last Updated: 12/12/15 (Ramified case under revision)