A note on the bundle underlying Opers
Luca Casarin

TL;DR
This paper clarifies that for any simple Lie algebra, the bundle underlying a $rak{g}$-Oper on a smooth curve depends solely on the curve itself and is derived from the canonical automorphism bundle, simplifying existing understanding.
Contribution
It provides a clear proof that the underlying bundle of a $rak{g}$-Oper is determined only by the curve and is induced by the canonical automorphism bundle, enhancing transparency in the literature.
Findings
The underlying bundle depends only on the curve.
It is induced by the canonical automorphism bundle.
The proof clarifies a well-known fact.
Abstract
In this note we write down a proof of the following well known fact, in order to make the literature more transparent. Let be a simple Lie algebra, then for any smooth curve , the bundle underlying any -Oper depends only on the curve and it is induced by the canonical bundle on .
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Taxonomy
TopicsGeometry and complex manifolds · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows
