Abstract:
This article contains a proof of the conjecture of Schwarzenberger that vector bundles on infinite-dimensional projective space P∞ split as the sum of line bundles, and a generalization to quasi-homogeneous projective varieties.
Bibliography: 7 titles.
This publication is cited in the following 23 articles:
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
Cristian Anghel, Springer Proceedings in Mathematics & Statistics, 263, Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 1, 2018, 385
S. M. Ermakova, “Ravnomernost vektornykh rassloenii konechnogo ranga na polnykh peresecheniyakh konechnoi korazmernosti v lineinykh ind-grassmanianakh”, Model. i analiz inform. sistem, 22:2 (2015), 209–218
I. B. Penkov, A. S. Tikhomirov, “On the Barth-Van de Ven-Tyurin-Sato theorem”, Sb. Math., 206:6 (2015), 814–848
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
S. M. Ermakova, “O prostranstve putei na polnykh peresecheniyakh v grassmanianakh”, Model. i analiz inform. sistem, 21:4 (2014), 35–46
A. L. Onishchik, E. G. Vishnyakova, “Locally free sheaves on complex supermanifolds”, Transformation Groups, 2013
Iustin Coandă, “A Simple Proof of Tyurin's Babylonian Tower Theorem”, Communications in Algebra, 40:12 (2012), 4668
I. B. Penkov, A. S. Tikhomirov, “Triviality of vector bundles on twisted ind-Grassmannians”, Sb. Math., 202:1 (2011), 61–99
Ivan Penkov, Alexander S. Tikhomirov, Progress in Mathematics, 270, Algebra, Arithmetic, and Geometry, 2009, 555
I. Coandă, G. Trautmann, “The Splitting Criterion of Kempf and the Babylonian Tower Theorem”, Communications in Algebra, 34:7 (2006), 2485
F. A. Bogomolov, A. L. Gorodentsev, V. A. Iskovskikh, Yu. I. Manin, V. V. Nikulin, D. O. Orlov, A. N. Parshin, V. Ya. Pidstrigach, A. S. Tikhomirov, N. A. Tyurin, I. R. Shafarevich, “Andrei Nikolaevich Tyurin (obituary)”, Russian Math. Surveys, 58:3 (2003), 597–605
E. Ballico, “Union of linear spaces in infinite-dimensional projective spaces and holomorphic vector bundles”, Results. Math, 43:3-4 (2003), 202
E. Ballico, “Topologically trivial holomorphic vector bundles on infinite-dimensional projective varieties”, Results. Math, 44:1-2 (2003), 35
László Lempert, “The Dolbeault complex in infinite dimensions I”, J. Amer. Math. Soc., 11:3 (1998), 485
H. Flenner, “Babylonian tower theorems for coverings”, Arch. Math, 57:3 (1991), 299
E. Graham Evans, Phillip Griffith, “Filtering cohomology and lifting vector bundles”, Trans. Amer. Math. Soc., 289:1 (1985), 321
Hubert Flenner, “Babylonian tower theorems on the punctured spectrum”, Math. Ann., 271:1 (1985), 153