A non-Kähler expanding Ricci soliton with a Kähler tangent cone at infinity

Abstract

We construct an example of an asymptotically conical (AC) non-Kähler expanding gradient Ricci soliton that has a Kähler tangent cone at infinity. This yields an example of a Kähler cone that can be desingularised by a smooth AC expanding gradient Ricci soliton but not by a smooth AC expanding gradient Kähler--Ricci soliton.

10 pages, comments welcome