Torelli theorem for the moduli space of framed bundles

Details Torelli theorem for the moduli space of framed bundles Torelli theorem for the moduli space of framed bundles

2008-08-14

arxiv.org/abs/0808.1996v1

Mathematics

Algebraic Geometry

12 pages

Scientific paper

Let X be an irreducible smooth complex projective curve of genus g>2, and let x be a fixed point. A framed bundle is a pair (E,\phi), where E is a vector bundle over X, of rank r and degree d, and \phi:E_x\to C^r is a non-zero homomorphism. There is a notion of (semi)stability for framed bundles depending on a parameter \tau>0, which gives rise to the moduli space of \tau-semistable framed bundles M^\tau. We prove a Torelli theorem for M^\tau, for \tau>0 small enough, meaning, the isomorphism class of the one-pointed curve (X,x), and also the integer r, are uniquely determined by the isomorphism class of the variety M^\tau.

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