Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669300 | Bulletin des Sciences Mathématiques | 2009 | 5 Pages |
Abstract
Fix a holomorphic line bundle ξ over a compact connected Riemann surface X of genus g, with g⩾2, and also fix an integer r such that degree(ξ)>r(2g−1). Let Mξ(r) denote the moduli space of stable vector bundles over X of rank r and determinant ξ. The Fourier–Mukai transform, with respect to a Poincaré line bundle on X×J(X), of any F∈Mξ(r) is a stable vector bundle on J(X). This gives an injective map of Mξ(r) in a moduli space associated to J(X). If g=2, then Mξ(r) becomes a Lagrangian subscheme.
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