GIT Stability, K-Stability and the Moduli Space of Fano Varieties

Canonical Kähler metrics and stability of algebraic varieties

“…The partial C 0 -estimates were later proved in different settings, starting with Donaldson-Sun's work in the Kähler-Einstein case, which leads to the solution of the YTD conjecture for smooth Fano manifolds in [24,66]. Moreover the partial C 0 -estimates has applications in constructing moduli spaces of smoothable Kähler-Einstein varieties and proving quasi-projectivity of the moduli spaces of KE manifolds, and these applications preclude the algebraic approach mentioned earlier (see [68]). We refer to [31,67] for surveys on related topics in this approach.…”