On complex deformations of Kähler-Ricci solitons (Q725648)

Despite the work of \textit{F. Podestà} and \textit{A. Spiro} [J. Geom. Anal. 25, No. 2, 1157--1174 (2015; Zbl 1322.53043)], not much is known about the existence of complex deformations of Kähler-Ricci solitons. In the present paper the author provides a necessary condition for the existence of polarized complex deformations of Kähler-Ricci solitons. This obstruction is expressed in terms of the harmonic part of the variation of the complex structure.