Kim–Rashkovskii's valuative invariance conjecture for Monge–Ampère masses

At least 5 years old · documented by

Let φ\varphi and ψ\psi be plurisubharmonic germs with isolated singularities at 0∈Cn0\in\mathbb{C}^n. For every divisorial valuation vv centered at 00, write v(φ)v(\varphi) for its generalized Lelong number on φ\varphi, and let en(φ,0)e_n(\varphi,0) denote the residual Monge–Ampère mass at 00. Kim–Rashkovskii's conjecture. If

v(φ)=v(ψ)v(\varphi)=v(\psi)

for every divisorial valuation vv centered at 00, then

en(φ,0)=en(ψ,0).e_n(\varphi,0)=e_n(\psi,0).

In other words, the conjecture asserts that residual Monge–Ampère masses are valuative invariants of plurisubharmonic singularities. It is proposed by Kim and Rashkovskii, and the source gives no resolution.

References

Primary source

Chi Li, “Analytical approximations and Monge-Ampère masses of plurisubharmonic singularities”, arXiv:2012.15599 (2021).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.