On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces

TL;DR

This paper classifies Gorenstein del Pezzo surfaces with vector fields that are K-stable and likely admit Kahler-Ricci solitons, and also presents new examples of Fano threefolds with such solitons.

Contribution

It provides a complete classification of K-stable Gorenstein del Pezzo surfaces with vector fields and introduces new Fano threefold examples admitting Kahler-Ricci solitons.

Findings

Classification of all K-stable Gorenstein del Pezzo pairs (X,v).

Identification of new Fano threefolds with Kahler-Ricci solitons.

Confirmation of the link between K-stability and existence of Kahler-Ricci solitons.

Abstract

We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces X and vector fields v which are K-stable in the sense of Berman-Nystrom and therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide some new examples of Fano threefolds admitting a Kahler-Ricci soliton.