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Jul 28, 2013 at 11:08 comment added Misha Verbitsky Understood. Now simplicity is never assumed in the definition of stability (see Lubcke-Teleman). Sorry for a confusion.
Jul 27, 2013 at 14:31 comment added Mircea but as I said Uhlenbeck and Yau assume simplicity in their definition of stability..
Jul 27, 2013 at 10:00 comment added diverietti You equip it by Uhlenbeck and Yau, indeed... That's the point of Misha's answer I think! On the other hand, this is certainly not the easy direction in the Kobayashi-Hitchin correspondence!
Jul 27, 2013 at 9:02 comment added Mircea How do you equip a stable bundle with a Hermitian-Einstein metric?
Jul 26, 2013 at 20:42 history edited Misha Verbitsky CC BY-SA 3.0
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Jul 26, 2013 at 18:41 history answered Misha Verbitsky CC BY-SA 3.0