Muñoz, VicenteOliveira, André G.Sánchez Hernández, Jonathan2023-06-182023-06-182015-041093-610610.4310/AJM.2015.v19.n2.a5https://hdl.handle.net/20.500.14352/24083Let C be a smooth projective curve of genus g >= 2 over C. Fix n >= 1, d is an element of Z. A pair (E, phi) over C consists of an algebraic vector bundle E of rank n and degree d over C 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. Let M-tau (n, d) be the moduli space of tau-polystable pairs of rank n and degree d over C. We prove that for a generic curve C, the moduli space M-tau (n, d) satisfies the Hodge Conjecture for n <= 4. For obtaining this, we prove first that M-tau (n, d) is motivated by C.engjournal articlehttp://intlpress.com/site/pub/pages/journals/items/ajm/content/vols/0019/0002/a005/body.htmlhttp://intlpress.com/http://arxiv.org/abs/1207.5120open access514515.1Moduli spacecomplex curvevector bundlemotivesHodge conjectureGeometríaTopología1204 Geometría1210 Topología