Jean-Pierre Serre, Prolongement de faisceaux analytiques coh ́erents, Ann. Inst. Fourier (Grenoble) 16 (1966), no. fasc. 1, 363–374. MR MR0212214 (35 #3088) p. 372 proves that there are infinitely many distinct holomorphic line bundles on $\mathbb{C}^2-0$.
Ben McKay
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