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Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties

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Abstract

Let V be an infinite-dimensional locally convex complex space, X a closed subset of P(V) defined by finitely many continuos homogeneous equations and E a holomorphic vector bundle on X with finite rank. Here we show that E is holomorphically trivial if it is topologically trivial and spanned by its global sections and in a few other cases.

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References

  1. E. Ballico. Lines in algebraic subsets of infinite-dimensional projective spaces and connectedness (preprint).

  2. S. Dineen. Cousin’s first problem on certain locally convex topological vector spaces. An. Acad. Brasil. Cienc. 48 (1976), 11–12.

    MathSciNet  MATH  Google Scholar 

  3. G. Elencwajg and O. Forster. Bounding cohomology groups of vector bundles on Pn. Math. Ann. 246 (1979/80), 251–270.

    Article  MathSciNet  Google Scholar 

  4. B. Kotzev. Vanishing of the first cohomology group of line bundles on complete intersections in infinite-dimensional projective space. Ph. D. thesis, University of Purdue, 2001.

  5. L. Lempert. The Dolbeaut complex in infinite dimension I. J. Amer. Math. Soc. 11 (1998), 485–520.

    Article  MathSciNet  MATH  Google Scholar 

  6. L. Lempert. The Dolbeaut complex in infinite dimension III. Sheaf cohomology in Banach spaces. Invent. Math. 142 (2000), 579–603.

    Article  MathSciNet  MATH  Google Scholar 

  7. P. Mazet. Analytic Sets in Locally Convex Spaces (North-Holland: Amsterdam, 1984).

    MATH  Google Scholar 

  8. C. Okonek, M. Schneider and H. Spindler. Vector Bundles on complex projective spaces (Progress in Math. 3, Birkhäuser: Boston — Basel — Stuttgart, 1980).

    Book  Google Scholar 

  9. E. Sato. On the decomposability of infinitely extendable vector bundles on projective spaces and Grassmann varieties. J. Math. Kyoto Univ. 17 (1977), 127–150.

    MathSciNet  MATH  Google Scholar 

  10. A. N. Tyurin. Vector bundles of finite rank over infinite varieties. Math. USSR Izvestija 10 (1976), 1187–1204.

    Article  Google Scholar 

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  1. Dept. of Mathematics, University of Trento, 38050, Povo, (TN), Italy

    E. Ballico

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  1. E. Ballico
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Correspondence to E. Ballico.

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Ballico, E. Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties. Results. Math. 44, 35–40 (2003). https://doi.org/10.1007/BF03322910

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  • DOI: https://doi.org/10.1007/BF03322910

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