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Torelli theorem for the moduli space of framed bundles

By Indranil Biswas, Tomas Gomez and Vicente Muñoz

Abstract

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).\u

Topics: Geometria algebraica
Publisher: Cambridge Univ Press
Year: 2020
DOI identifier: 10.1017/S0305004109990417
OAI identifier: oai:www.ucm.es:17012
Provided by: EPrints Complutense
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