Stability of the poincare bundle

Balaji, V. ; Brambila-Paz, L. ; Newstead, P. E. (1997) Stability of the poincare bundle Mathematische Nachrichten, 188 (1). pp. 5-15. ISSN 0025-584X

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Let C be a nonsingular projective curve of genus g ≥ 2 defined over the complex numbers, and let Mξ denote the moduli space of stable bundles of rank n and determinant ξ on C, where ξ is a line bundle of degree don C and n and d are coprime. It is shown that a universal bundle Uξ on C × Mξ is stable with respect to any polarisation on C × Mξ. Similar results are obtained for the case where the determinant is not fixed and for the bundles associated to the universal bundles by irreducible representations of GL(n, C). It is shown further that the connected component of the moduli space of bundles with the same Hilbert polynomial as Uξ on C × Mξ containing Uξ is isomorphic to the Jacobian of C.

Item Type:Article
Source:Copyright of this article belongs to John Wiley and Sons, Inc.
Keywords:Stable Bundles; Moduli Space; Universal Bundle
ID Code:996
Deposited On:25 Sep 2010 06:50
Last Modified:16 May 2016 12:10

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