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On the Picard bundle
Authors:Indranil Biswas  GV Ravindra
Institution:a School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
b Mathematics Department, Indian Institute of Science, Bangalore 560012, India
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 FMξ(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.
Keywords:14D20  14D21
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