Linear ind-Grassmannians

Abstract

We consider ind-varieties obtained as direct limits of chains of embeddings $X_1\stackrel{{\varphi }_1}{\hookrightarrow }\dots \stackrel{{\varphi }_{m-1}}{\hookrightarrow }{X}_m\stackrel{{\varphi }_m}{\hookrightarrow }{X}_{m+1}\stackrel{{\varphi }_{m+1}}{\hookrightarrow }\dots$, where each $X_m$ is a Grassmannian or an isotropic Grassmannian (possibly mixing Grassmannians and isotropic Grassmannians), and the embeddings ${\varphi }_m$ are linear in the sense that they induce isomorphisms of Picard groups. We prove that any such ind-variety is isomorphic to one of certain standard ind-Grassmannians and that the latter are pairwise non-isomorphic ind-varieties.

arXiv commentKeywords: Grassmannian, ind-variety, linear morphism of algebraic varieties; Pages no. : 22; Bibliography : 8 items