Abstract: The theory of complements, also known as Shokurov's program, is introduced by Shokurov when he proved the existence of flips for threefolds. In this talk, I will introduce Shokurov's complements conjecture, that is the existence of ($\epsilon,n$)-complements. Then I will show some applications of the conjecture. Finally, I will give a sketch of the proof of the conjecture for surfaces. This is a joint work with Jingjun Han.
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