Toric Generalized K\"ahler-Ricci Solitons with Hamiltonian 2-form

TL;DR

This paper derives explicit solutions for generalized K"ahler-Ricci solitons on 4D toric K"ahler orbifolds with Hamiltonian 2-forms, including new examples like weighted projective planes.

Contribution

It reduces the soliton equation to ODEs on certain orbifolds and provides explicit solutions, including new examples, which advances understanding of these geometric structures.

Findings

Explicit solutions on labeled triangles and quadrilaterals

New examples of K"ahler-Ricci solitons on weighted projective planes

Reduction of PDEs to ODEs under Hamiltonian 2-form assumption

Abstract

We show that the generalized K\"ahler-Ricci soliton equation on 4-dimensional toric K\"ahler 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 K\"ahler-Ricci solitons of weighted projective planes as well as new examples.