I've been recently studying the classification of principal G-bundles over elliptic curves. Specifically I've been using the paper by Friedman, Morgan and Witten "Principal G-Bundles over elliptic curves".
I've been trying to relate how the classification of principal G-bundles over the Torus $T^2$ relates to the classification over a Torus embedded in the complex projective plane via the Weierstraß $\wp$-function:
$z\to (1,\wp(z),\wp'(z))$
Intuitivly I'd say they should yield the same result. However my main problem arises that the classifications are done differently, or at least it seems to me that way (Isomorphisms vs. S-Equivalence) and I'm unsure of how to relate these two?
Ultimately I'm interested in 6-dimensional cases ($T^6$ and it's counterpart), but I want to understand the 2 dimensional case first before moving on.
I'm thankful for any pointers or clarifications on this matter.
