Given an elliptic curve , flat Ek-bundles over are in one-to-one correspondence with smooth del Pezzo surfaces of degree 9 − k containing as an anti-canonical curve. This correspondence was generalized to Lie groups of any type. In
this article, we show that there is a similar correspondence between del Pezzo surfaces of degree 0 with an Ad-singularity containing as an anti-canonical curve and Kac–Moody Ek-bundles over with k = 8−d. In the degenerate case where surfaces are rational elliptic surfaces, the corresponding Ek-bundles over can be reduced to Ek-bundles.