Kähler-Ricci Tangent Flows are Infinitesimally Algebraic

Abstract

We show that any tangent cone of a singular shrinking Kähler-Ricci soliton is a normal affine algebraic variety. Moreover, the regular set of such a tangent cone in the metric sense coincides with the regular set in the algebraic sense. Along the way, we give a parabolic proof of Hörmander's $L^2$ estimate, which can be used to solve the $\overline{\partial }$-equation on any singular shrinking Kähler-Ricci soliton.

Minor corrections and simplifications