The Lee–Gauduchon Cone on Complex Manifolds

Liviu Ornea () and Misha Verbitsky ()
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Liviu Ornea: University of Bucharest, Faculty of Mathematics and Informatics
Misha Verbitsky: Instituto Nacional de Matemática Pura e Aplicada (IMPA)

A chapter in Real and Complex Geometry, 2025, pp 237-250 from Springer

Abstract: Abstract Let M be a compact complex n-manifold. A Gauduchon metric is a Hermitian metric whose fundamental 2-form ω $$\omega $$ satisfies the equation d d c ( ω n −1 ) = 0 $$dd^c(\omega ^{n-1})=0$$ . 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 ) $$d^c(\omega ^{n-1})$$ is a closed ( 2 n −1 ) $$(2n-1)$$ -form; the set of cohomology classes of all such forms, called the Lee-Gauduchon cone, is a convex cone, superficially similar to the Kähler cone. We prove that the Lee-Gauduchon cone is a bimeromorphic invariant, and compute it for several classes of non-Kähler manifolds.

Keywords: Positive current; Pseudo-effective cone; Bott–Chern cohomology; Aeppli cohomology; 53C55; 32H04 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-92297-8_11

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DOI: 10.1007/978-3-031-92297-8_11

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