  We show that any tangent cone of a singular shrinking K\"ahler-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 as a variety.
Along the way, we establish a parabolic proof of H\"ormander's $L^{2}$
estimate, which can be used to solve the $\overline{\partial}$-equation on any
singular shrinking K\"ahler-Ricci soliton.

Differential Geometry