Failure of the local decay formula for Arnold multiplicities under twisted Kähler--Ricci flow
Year: 2026
Type: preprint
Abstract: Di Nezza--Guedj--Lu asked whether local Arnold multiplicities under maximal weak twisted Kähler--Ricci flow with fixed cohomology class satisfy $λ(φ_t,x)=\max\{λ(φ_0,x)-t,0\}$. We construct counterexamples with analytic initial singularities in every dimension $n\ge2$. On the Hirzebruch surface $\mathbb F_e$, $e\ge2$, the initial current $[S]+(e+1)[F]$ yields $λ(φ_t,x)=1/2-t/e$ for $x\in S\setminus F$ and $0
Source: arXiv (Cornell University)
Author: Qin, Xiangsen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204875218