Non-standard Holomorphic Structures on Line Bundles over the Quantum Projective Line

In this paper we study non-standard holomorphic structures on line bundles over the quantum projective line $\mathbb{C}{P}_q^1$. We show that there exist infinitely many non-gauge equivalent holomorphic structures on those line bundles. This gives a negative answer to a question raised by Khalkhali, Landi, and Van Suijlekom in 2011.