Talk:Kobayashi–Hitchin correspondence
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Cite Hitchin's 1979 paper?
[edit]The review on Zentralblatt, by Hitchin, of the Uhlenbeck-Yau paper gives a reference to a 1979 paper:
"It was suggested by the reviewer [Nonlinear problems in geometry, Proc. Sixth Int. Symp., Sendai/Japan (1979; Zbl 0433.53002)] and independently S. Kobayashi [Proc. Jap. Acad., Ser. A 58, 158-162 (1982; Zbl 0538.32021)] that stability of a holomorphic vector bundle should be a necessary and sufficient condition for the existence of such a connection. Necessity was proved by M. Lübke [Manuscr. Math. 42, 245-257 (1983; Zbl 0558.53037)]. Sufficiency is proved in this paper, motivating evidence having been always present in the theorem of M. S. Narasimhan and C. S. Seshadri, who had long ago proved the theorem for curves [Ann. Math., II. Ser. 82, 540-567 (1965; Zbl 0178.048)], the more recent fact that the solutions of the self-duality equations on S4 pull back to be Hermitian-Yang-Mills on the twistor space CP3, and the proof of the theorem for algebraic surfaces by S. K. Donaldson [Proc. Lond. Math. Soc., III. Ser. 50, 1-26 (1985; Zbl 0529.53018)]." — Preceding unsigned comment added by 2A01:E0A:24:2900:2EE2:EC49:9C3D:65B1 (talk) 08:05, 8 December 2020 (UTC)
Things left to do
[edit]I have expanded the history section, added a precise statement of the theorem, and listed all the important generalisations and proximate notions. The article is in a fairly good state now, and is missing some key examples. If it is to stay as mid importance it should also have added some more layman friendly discussion of the impact of the theorem.Tazerenix (talk) 03:03, 11 March 2021 (UTC)