Motives and the Hodge Conjecture for moduli spaces of pairs

Vicente Muñoz, André Oliveira, Jonathan Sánchez

Let $C$ be a smooth projective curve of genus $g\ge 2$ over $\mathbb{C}$. Fix $n\ge 1$, $d\in \mathbb{Z}$. A pair $(E,\varphi )$ over $C$ consists of an algebraic vector bundle $E$ of r…