On the classification of Kähler–Ricci solitons on Gorenstein del Pezzo surfaces

2017/05/31 by Jacob Cable, Hendrik Süß
Mathematics · #Advanced Algebra and Geometry #Fano plane #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics #Pure mathematics #math.AG #math.DG #msc:14J45 #msc:14L30 #msc:32Q20 #msc:53C25

paper · pdf · doi:10.1007/s40879-017-0204-y

published as European Journal of Mathematics (2018) 4: 137-161 · 21 pages, ancillary files containing calculations in SageMath; minor corrections

openalex created_date 2017/05/19 · openalex publication_date 2017/12/11 · arxiv created 2018/03/10 · arxiv updated 2018/03/13 · openalex updated_date 2026/08/05

Abstract

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

Citations

• Kahler geometry on toric manifolds, and some other manifolds with large symmetry
• Compact Moduli Spaces of Del Pezzo Surfaces and Kähler-Einstein metrics
• Classification of Fano 3-folds with B2?2
• Algebraic Geometry