Year: 2026
Type: preprint
Abstract: We demonstrate that Kähler-Ricci flow on a Fano surface decomposes as a symplectic deflation along a plurianticanonical divisor plus an exact symplectic deformation in the divisor complement. We apply this decomposition to the study of certain projective bundles. We establish the optimal decay rate in the setting of Song, Székelyhidi, and Weinkove for a family of toric metrics which match the cohomological profile of Kähler-Ricci flow. In doing so, we identify a $C^2$-obstruction to proving the optimal decay rate in the setting of ruled toric surfaces. We present these ideas as a new symplectic-topological approach to the study of Kähler-Ricci flow.
Source: arXiv (Cornell University)
Author: Van Why, Randall R.
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223015101