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arXiv · 2212.01695

Real Slices of ${\rm SL}(r,\mathbb{C})$-Opers

Indranil Biswas·Sebastian Heller·Laura P. Schaposnik
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Abstract

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.

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Indranil Biswas, Sebastian Heller, Laura P. Schaposnik. 2022-12-03. Real Slices of ${\rm SL}(r,\mathbb{C})$-Opers. https://doi.org/10.3842/sigma.2023.067

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