Abstract:
The Barth-Van de Ven-Tyurin-Sato Theorem states that any finite-rank vector bundle on the complex projective ind-space P∞ is isomorphic to a direct sum of line bundles. We establish sufficient conditions on a locally complete linear ind-variety X which ensure that the same result holds on X. We then exhibit natural classes of locally complete linear ind-varieties which satisfy these sufficient conditions.
Bibliography: 18 titles.
We acknowledge the support and hospitality of the Max Planck Institute for Mathematics in Bonn where the present paper was conceived. We also acknowledge partial support from the DFG through Priority Program "Representation Theory" (SPP 1388) at Jacobs University Bremen.
\Bibitem{PenTik15}
\by I.~B.~Penkov, A.~S.~Tikhomirov
\paper On the Barth-Van de Ven-Tyurin-Sato theorem
\jour Sb. Math.
\yr 2015
\vol 206
\issue 6
\pages 814--848
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This publication is cited in the following 4 articles:
Arijit Mukherjee, D.S. Nagaraj, “Diagonal property and weak point property of higher rank divisors and certain Hilbert schemes”, Bulletin des Sciences Mathématiques, 198 (2025), 103541
E Ballico, “Extending Infinitely Many Times Arithmetically Cohen–Macaulay and Gorenstein Subvarieties of Projective Spaces”, The Quarterly Journal of Mathematics, 73:2 (2022), 701
M. V. Ignatyev, I. Penkov, “Ind-Varieties of Generalized Flags: A Survey of Results”, Journal of Mathematical Sciences, 248:3 (2020), 255–302
S. M. Ermakova, “Finite-Rank Vector Bundles on Complete Intersections of Finite Codimension in the Linear Ind-Grassmannian”, Math. Notes, 98:5 (2015), 852–856
Citation in format AMSBIB
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