The Lee--Gauduchon cone on complex manifolds

2024/11/08 by Ornea, Liviu, Verbitsky, Misha · 1 citation
#32H04 #53C55 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.05595

Abstract

Let M be a compact complex n-manifold. A Gauduchon metric is a Hermitian metric whose fundamental 2-form ω satisfies the equation dd^c(ω^n-1)=0. Paul Gauduchon has proven that any Hermitian metric is conformally equivalent to a Gauduchon metric, which is unique (up to a constant multiplier) in its conformal class. Then d^c(ω^n-1) is a closed (2n-1)-form; the set of cohomology classes of all such forms, called the Lee-Gauduchon cone, is a convex cone, superficially similar to the Kahler cone. We prove that the Lee-Gauduchon cone is a bimeromorphic invariant, and compute it for several classes of non-Kahler manifolds.

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• Singular Gauduchon Conjecture

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