Muñoz, Vicente2023-06-202023-06-2020090305-004110.1017/S0305004108002156https://hdl.handle.net/20.500.14352/50181Let X be a smooth projective curve of genus g >= 2 over C. A pair (E, phi) over X consists of an algebraic vector bundle E over X and a section phi is an element of H(0)(E). There is a concept of stability for pairs which depends on a real parameter tau. Here we prove that the third cohomology groups of the moduli spaces of tau-stable pairs with fixed determinant and rank n >= 2 are polarised pure Hodge structures, and they are isomorphic to H(1) (X) with its natural polarisation (except in very few exceptional cases). This implies a Torelli theorem for such moduli spaces. We recover that the third cohomology group of the moduli space of stable bundles of rank n >= 2 and fixed determinant is a polarised pure Hodge structure, which is isomorphic to H(1) (X). We also prove Torelli theorems for the corresponding moduli spaces of pairs and bundles with non-fixed determinant.engjournal articlehttp://journals.cambridge.org/abstract_S0305004108002156http://www.cambridge.orgrestricted access512.7Ppolystable pairSemistable vector bundlesSemistable tripleModuli spaceSmooth projective curveTorelli theoremHodge structureGeometria algebraica1201.01 Geometría Algebraica