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Torelli theorem for the moduli space of framed bundles


Biswas, Indranil and Gomez, Tomas and Muñoz, Vicente (2010) Torelli theorem for the moduli space of framed bundles. Mathematical Proceedings of the Cambridge Philosophical Society, 148 (3). pp. 409-423. ISSN 0305-0041

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Let X be an irreducible smooth complex projective curve of genus g >= 2, and let x is an element of X be a fixed point. Fix r > 1, and assume that g > 2 if r = 2. A framed bundle is a pair (E, phi), where E is coherent sheaf on X of rank r and fixed determinant xi, and phi: E(x) > 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).

Item Type:Article
Uncontrolled Keywords:Framed bundles; Smooth curves; Moduli
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:17012

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