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This article is cited in 2 scientific papers (total in 2 papers)
Holomorphic bundles on diagonal Hopf manifolds
M. S. Verbitsky Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Abstract:
We show that every stable holomorphic bundle on the Hopf manifold $M=(\mathbb C^n\setminus0)/\langle A\rangle$ with $\dim M\geqslant 3$, where $A\in\operatorname{GL}(n,\mathbb C)$ is a diagonal linear operator with all eigenvalues satisfying $|\alpha_i|<1$, can be lifted to a $\widetilde G_F$-equivariant coherent sheaf on $\mathbb C^n$, where $\widetilde G_F\cong(\mathbb C^*)^l$ is a commutative Lie group acting on $\mathbb C^n$ and containing $A$. This is used to show that all bundles on $M$ are filtrable, that is, admit a filtration by a sequence $F_i$ of coherent sheaves with all subquotients $F_i/F_{i-1}$ of rank $1$.
Received: 30.08.2005 Revised: 16.06.2006
Citation:
M. S. Verbitsky, “Holomorphic bundles on diagonal Hopf manifolds”, Izv. RAN. Ser. Mat., 70:5 (2006), 13–30; Izv. Math., 70:5 (2006), 867–882
Linking options:
https://www.mathnet.ru/eng/im616https://doi.org/10.1070/IM2006v070n05ABEH002331 https://www.mathnet.ru/eng/im/v70/i5/p13
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Abstract page: | 890 | Russian version PDF: | 362 | English version PDF: | 17 | References: | 58 | First page: | 3 |
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