Normalized volume and F-volume reduction conjecture

Let x(X,Δ)x\in (X,\Delta) be a klt singularity over characteristic 00, and let (xp(Xp,Δp))(x_p\in (X_p,\Delta_p)) be its reduction modulo p0p\gg 0. Reduction conjecture.

vol^(x,X,Δ)=limpFvol(xp,Xp,Δp).\widehat{\operatorname{vol}}(x,X,\Delta)=\lim_{p\to\infty}\operatorname{Fvol}(x_p,X_p,\Delta_p).

This conjecture proposes that normalized volume in characteristic zero is recovered as the limit of the FF-volumes of reductions in positive characteristic.

Sources & referencesView supporting material

Primary source

Chi Li, Yuchen Liu and Chenyang Xu, “A Guided Tour to Normalized Volume”, arXiv:1806.07112 (2019).

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