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Stability of the Poincaré Bundle

✍ Scribed by V. Balaji; L. Brambila-Paz; P. E. Newstead

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
506 KB
Volume
188
Category
Article
ISSN
0025-584X

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✦ Synopsis

Let C be a nonsingular projective curve of genus g > 2 defined over the complex numbers, and let Me denote the moduli space of stable bundles of rank n and determinant ( on C , where 5 is a line bundle of degree d on C and n and d are coprime. It is shown that a universal bundle Uc on C x Me is stable with respect to any polarisation on C x M E . 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 U, on C x Mc containing Uc is isomorphic to the Jacobian of C.

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