Pure and Applied Mathematics Quarterly

Volume 10 (2014)

Number 2

Special Issue: In Memory of Andrey Todorov, Part 3 of 3

Linear Ind-grassmannians

Pages: 289 – 323

DOI: http://dx.doi.org/10.4310/PAMQ.2014.v10.n2.a5

Authors

Ivan Penkov (School of Engineering and Science, Jacobs University, Bremen, Germany)

Alexander S. Tikhomirov (Department of Mathematics, State Pedagogical University, Yaroslavl, Russia)

Abstract

We consider ind-varieties obtained as direct limits of chains of embeddings $X_1 \overset{\varphi_1}{\hookrightarrow} \dots \overset{\varphi_{m - 1}}{\hookrightarrow}X_m \overset{\varphi_m}{\hookrightarrow} X_{m+1} \overset{\varphi_{m + 1}}{\hookrightarrow} \dots$, 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.

Keywords

grassmannian, ind-variety, linear morphism of algebraic varieties

2010 Mathematics Subject Classification

14A10, 14M15

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