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Stability of the Poincaré Bundle
Author(s) -
Balaji V.,
BrambilaPaz L.,
Newstead P. E.
Publication year - 1997
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19971880102
Subject(s) - mathematics , moduli space , coprime integers , invertible matrix , pure mathematics , genus , rank (graph theory) , line bundle , irreducible component , bundle , combinatorics , mathematical analysis , differential algebraic equation , ordinary differential equation , botany , materials science , composite material , biology , differential equation
Let C be a nonsingular projective curve of genus g ≥2 defined over the complex numbers, and let M ξ 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 U ξ on C × M ξ is stable with respect to any polarisation on C × M ξ . 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 ξ on C × M ξ containing U ξ is isomorphic to the Jacobian of C .