Motives and the Hodge conjecture for moduli spaces of pairs

Vicente Muñoz, André G. Oliveira, Jonathan Sánchez
2015 Asian Journal of Mathematics  
Let C be a smooth projective curve of genus g ≥ 2 over C. Fix n ≥ 1, d ∈ Z. A pair (E, φ) over C consists of an algebraic vector bundle E of rank n and degree d over C and a section φ ∈ H 0 (E). There is a concept of stability for pairs which depends on a real parameter τ . Let Mτ (n, d) be the moduli space of τ -polystable pairs of rank n and degree d over C. We prove that for a generic curve C, the moduli space Mτ (n, d) satisfies the Hodge Conjecture for n ≤ 4. For obtaining this, we prove first that Mτ (n, d) is motivated by C.
doi:10.4310/ajm.2015.v19.n2.a5 fatcat:gyylobfub5fzdmdeiczjfcyk24