Torelli theorem for the moduli space of framed bundles

Biswas, I. ; Gomez, T. ; Munoz, V. (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 ∈ X 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 ξr, and φ : Ex→ Cr 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 Mτ. We prove a Torelli theorem for Mτ, 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 Mτ.

Item Type:Article
Source:Copyright of this article belongs to Cambridge University Press.
ID Code:3631
Deposited On:18 Oct 2010 10:17
Last Modified:20 May 2011 04:30

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