Kodaira dimension & the Yamabe problem, II

Michael Albanese; Claude LeBrun

doi:10.4310/CAG.2023.v31.n10.a3

Kodaira dimension & the Yamabe problem, II

Michael Albanese
, Claude LeBrun

Mathematics

University of Adelaide

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

Abstract

For compact complex surfaces (M4, J) of Kähler type, it was previously shown [30] that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M, J). In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from [2] that explains why the exclusion of class VII is essential here.

Original language	English
Pages (from-to)	2387-2411
Number of pages	25
Journal	Communications in Analysis and Geometry
Volume	31
Issue number	10
DOIs	https://doi.org/10.4310/CAG.2023.v31.n10.a3
State	Published - 2023

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10.4310/CAG.2023.v31.n10.a3

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title = "Kodaira dimension \& the Yamabe problem, II",

abstract = "For compact complex surfaces (M4, J) of K{\"a}hler type, it was previously shown [30] that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M, J). In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from [2] that explains why the exclusion of class VII is essential here.",

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AU - Albanese, Michael

AU - LeBrun, Claude

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AB - For compact complex surfaces (M4, J) of Kähler type, it was previously shown [30] that the sign of the Yamabe invariant Y (M) only depends on the Kodaira dimension Kod(M, J). In this paper, we prove that this pattern in fact extends to all compact complex surfaces except those of class VII. In the process, we also reprove a result from [2] that explains why the exclusion of class VII is essential here.

UR - https://www.scopus.com/pages/publications/85201659764

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DO - 10.4310/CAG.2023.v31.n10.a3

M3 - Article

AN - SCOPUS:85201659764

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VL - 31

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JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 10

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Kodaira dimension & the Yamabe problem, II

Abstract

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