https://neckpinch.com/authors/xiangsen-qin/New arXiv papers by Xiangsen Qin, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2608.30302/arxiv:2608.30302Mon, 31 Aug 2026 00:00:00 GMTXiangsen Qin — Di Nezza–Guedj–Lu asked whether local Arnold multiplicities under maximal weak twisted Kähler–Ricci flow with fixed cohomology class satisfy λ(φₜ,x)=max\λ(φ₀,x)−t,0\. We construct counterexamples with analytic initial singularities in every dimension n≥2. On the Hirzebruch surface Fₑ, e≥2, the initial current [S]+(e+1)[F] yields λ(φₜ,x)=1/2-t/e for x∈ S∖ F and 0<t<e/2, where S is the negative section and F a fibre. Products with smooth stationary factors give higher-dimensional examples. The Zariski negative part of S\+F\, the reduced support class, forces extra divisor mass. For pure divisorial data with simple normal crossings support, a smooth semipositive representative of the reduced support class's positive part gives exact short-time formulas. On one surface we construct flows with identical initial current germs, background data and global initial Arnold multiplicity, but different local rates.Ricci flowKähler–Ricci flowSingularitiesKähler geometry