2011/03/24 by Éveline Legendre, Legendre, Eveline, Christina W. Tønnesen-Friedman +1
Mathematics · #Geometry and complex manifolds #Advanced Topics in Algebra #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.1103.4706
We show that the generalized Kähler-Ricci soliton equation on 4-dimensional toric Kähler orbifolds reduces to ODEs assuming there is a Hamiltonian 2-form. This leads to an explicit resolution of this equation on labeled triangles and convex labeled quadrilaterals. In particular, we give the explicit expression of the Kähler-Ricci solitons of weighted projective planes as well as new examples.