Real Slices of SL(𝑟, ℂ)-Opers

Abstract

Through the action of an anti-holomorphic involution 𝜎 (a real structure) on a Riemann surface 𝛸, we consider the induced actions on SL(𝑟, ℂ)-opers and study the real slices fixed by such actions. By constructing this involution for different descriptions of the space of SL(𝑟, ℂ)-opers, we can 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.