On Strongly Gauduchon Metrics of Compact Complex Manifolds

Jian Xiao

doi:10.1007/s12220-014-9502-5

On Strongly Gauduchon Metrics of Compact Complex Manifolds

Jian Xiao^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones (Formula presented.) in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence result of strongly Gauduchon metrics on a compact complex manifold which is fibered over a compact complex curve. In particular, if a compact complex manifold (Formula presented.) has a topologically essential fibration over a compact complex curve, and if the generic fibers satisfy the (Formula presented.)-lemma, then (Formula presented.) admits strongly Gauduchon metrics.

Original language	English (US)
Pages (from-to)	2011-2027
Number of pages	17
Journal	Journal of Geometric Analysis
Volume	25
Issue number	3
DOIs	https://doi.org/10.1007/s12220-014-9502-5
State	Published - Jul 20 2015

Keywords

Fibration
Positive cones
Positive currents
Proper modification
Strongly Gauduchon metrics

ASJC Scopus subject areas

Geometry and Topology

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10.1007/s12220-014-9502-5

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abstract = "In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones (Formula presented.) in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence result of strongly Gauduchon metrics on a compact complex manifold which is fibered over a compact complex curve. In particular, if a compact complex manifold (Formula presented.) has a topologically essential fibration over a compact complex curve, and if the generic fibers satisfy the (Formula presented.)-lemma, then (Formula presented.) admits strongly Gauduchon metrics.",

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AU - Xiao, Jian

PY - 2015/7/20

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N2 - In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones (Formula presented.) in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence result of strongly Gauduchon metrics on a compact complex manifold which is fibered over a compact complex curve. In particular, if a compact complex manifold (Formula presented.) has a topologically essential fibration over a compact complex curve, and if the generic fibers satisfy the (Formula presented.)-lemma, then (Formula presented.) admits strongly Gauduchon metrics.

AB - In this paper, we study strongly Gauduchon metrics on compact complex manifolds. We study the cohomology cones (Formula presented.) in the de Rham cohomology groups generated by all strongly Gauduchon metrics and its direct images under proper modifications. We also study the moduli of strongly Gauduchon manifolds. We prove an existence result of strongly Gauduchon metrics on a compact complex manifold which is fibered over a compact complex curve. In particular, if a compact complex manifold (Formula presented.) has a topologically essential fibration over a compact complex curve, and if the generic fibers satisfy the (Formula presented.)-lemma, then (Formula presented.) admits strongly Gauduchon metrics.

KW - Fibration

KW - Positive cones

KW - Positive currents

KW - Proper modification

KW - Strongly Gauduchon metrics

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On Strongly Gauduchon Metrics of Compact Complex Manifolds

Abstract

Keywords

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