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Abstract For a simple, simply connected complex affine algebraic group 𝐺, we prove the existence of a flat projective connection on the bundle of nonabelian theta functions on the moduli spaces of semistable parabolic 𝐺-bundles for families of smooth projective curves with marked points.more » « less
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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.more » « less
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