This is an expository paper dedicated to professor L. Nirenberg for his 85th birthday. First I will discuss my joint works with
Z. Zhang and J. Song on the singularity formation of Kähler-Ricci flow. Secondly, I will show a fully nonlinear equation,
scalar V-soliton equation (cf. Section 4, (14)), and some basic results about it.
This equation was introduced by G. La Nave and myself in studying the singularity formation of Kähler-Ricci flow.
I will also show how this new equation can be applied to studying the singularity formation at finite time.