Through the action of an anti-holomorphic involution $\sigma$ (a real structure) on a Riemann surface $X$, we consider the induced actions on ${ \rm SL}(r,\mathbb{ C})$-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of ${ \rm SL}(r,\mathbb{ C})$-opers, we are able to give a natural parametrization of the fixed point locus via differentials on the Riemann surface, which in turn allows us to study their geometric properties.
Categories: math.DG