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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 148, Issue 3
  • May 2010, pp. 409-423

Torelli theorem for the moduli space of framed bundles

  • I. BISWAS (a1), T. GÓMEZ (a2) and V. MUÑOZ (a2)
  • DOI: http://dx.doi.org/10.1017/S0305004109990417
  • Published online: 26 November 2009
Abstract
Abstract

Let X be an irreducible smooth complex projective curve of genus g ≥ 2, and let xX be a fixed point. Fix r > 1, and assume that g > 2 if r = 2. A framed bundle is a pair (E, φ), where E is coherent sheaf on X of rank r and fixed determinant ξ, and φ: Exr is a non–zero homomorphism. There is a notion of (semi)stability for framed bundles depending on a parameter τ > 0, which gives rise to the moduli space of τ–semistable framed bundles τ. We prove a Torelli theorem for τ, for τ > 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 τ.

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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