K-stability of Fano varieties

In mathematics, and in particular algebraic geometry, K-stability is an algebro-geometric stability condition for projective algebraic varieties and complex manifolds. K-stability is of particular importance for the case of Fano varieties, where it is the correct stability condition to allow the formation of moduli spaces, and where it precisely characterises the existence of Kähler–Einstein metrics.

Source: Wikipedia — K-stability of Fano varieties (CC BY-SA 4.0)