Triviality of Vector Bundles on Sufficiently Twisted Ind-grassmannians
نویسنده
چکیده
Twisted ind-Grassmannians are ind-varieties G obtained as direct limits of Grassmannians G(rm, V m), for m ∈ Z>0, under embeddings φm : G(rm, V m) → G(rm+1, V m+1) of degree greater than one. It has been conjectured in [PT] and [DP] that any vector bundle of finite rank on a twisted ind-Grassmannian is trivial. We prove this conjecture under the assumption that the ind-Grassmannian G is sufficiently twisted, i.e. that limm→∞ rm deg φ1...deg φm = 0. 2000 Mathematics Subject Classification, Primary 14M15, (Secondary 14J60, 32L05).
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تاریخ انتشار 2008